You should definitely endeavor to get ASIO working; it shouldn't be a big deal to sort that out. My first guess would be that the output assignment of you Master bus got fouled up by changing driver names.
 
Incidentally, if you have to use WASAPI for the time being, you'll get the best result with WASAPI Exclusive mode which allows a 3ms buffer size vs. 10ms, IIRC, for WASAPI Shared mode.

Hi,
 
Apologies for bringing this up again. I saw what you guys have advised - to use ASIO. Hence I changed from WASAPI to ASIO. When I changed to ASIO, I was only given the option to select "Generic low latency ASIO driver speakers".  And when that was selected, I cannot hear any sound. Restarting SONAR does not resolve the issue.
 

 
Then when I switched back to WASAPI shared, i have the option to select the TASCAM interface.
 

 
I tried to use WASAPI exclusive, and I repeatedly get this error message:
 

 
I'm also not sure if the issue is related to the drivers, but ever since installing the audio interface, I get fairly frequent issues such as:
 
- Buzzing sounds for certain VSTs. Some buzzing sounds are very loud and distorted and are very reproducible when I I press the keys on the keyboard. Others are softer but still pretty obvious.
- Sounds suddenly become silent. I have experienced when a new MIDI track appears, suddenly all the tracks cease to produce any sounds. 
 
For the first case, reloading the VST solved the issue (but still a hassle). For the second case, I managed to resolve it by repeatedly toggle in and out of the Preference window.
 
I'm willing to monitor this issue again if I'm able to resolve the driver issue above.
 
Sorry again; if there's any help for this it will be appreciated. 

I would:
 
- Exit SONAR
- Rename AUD.INI in C:\Users\<username>\AppData\Roaming\Cakewalk\SONAR Platinum\AUD.INI
- Power down your interface, and uninstall the Tascam drivers.
- Reboot with the interface still down and reinstall the Tascam drivers.
- Shut down your PC and do a cold boot with your interface running (always have USB interfaces powered up when booting once the drivers are installed).
- Restart SONAR (it will automatically build a new default AUD.INI), reset driver mode to ASIO if necessary, and check if you now have US-2x2 ASIO drivers available as Playback and Record Timing Masters.
 

May want to uninstall the "Generic low latency ASIO driver" too. I believe that is something installed by another DAW. It is not a manufacturer supplied ASIO driver.

You have installed your Tascam driver incorrectly. That Generic Drive will take over if you don't follow the instructions closely  during installation. You have plugged in the interface before it asked you to. A  least this is the case with my Tascam and Focusrite drivers.
 
If you plug in a USB device Windows will install a generic driver. Fine if it's a mouse or USB drive. Not good for Audio Interfaces. 
 
Install the driver and wait for the instructions to tell you to connect your interface. It will also be best to ignore any Windows pop up messages too.. 

Hi,
I've tried what brundlefly advised - uninstalled / reinstalled the driver. Renamed aud.ini etc. I also deleted the "Generic low latency ASIO driver" too. 
So after reinstallation and launching SONAR, I could see that choosing ASIO driver now allows me to select the TASCAM 2x2 drivers in playback/recording.
 
There is now a new problem I'm having. Whenever I launch SONAR, I can't play music on my browser or media player. When I open up a new browser, I get the following error message when launching SONAR: "There are no audio devices for the current driver model on your system. Please go to Edit/Preferences/Audio/Playback and Recording etc." and true enough no audio. The moment I close the browser, and relaunch SONAR, it seemed to work again.
 
So what I did was, in the sound driver properties, I unchecked "Allow applications to take exclusive control of this device". I rebooted my computer - problem still remained. 
 
Suspecting it could be a SONAR issue, inside SONAR, I also checked "share drivers with other programs". I also restarted SONAR - problem still remained. 
 
I was more certain it is a SONAR issue, because I was able to play music on my browser and the media player at the same time. The moment I launch SONAR everything went haywire. 

After which I tried to experiment by going into WASAPI shared / WASAPI exclusive / MME32 etc. I got the same error messages as before: "The following drivers either do not support the current audio format etc..." And again no sound in all the drivers.
 
Now the problem just got worse. After this brief "experiment", I could not find any drivers when I switched back to ASIO. Not only that, even after closing SONAR, I couldn't play anything in my browser, or media player. When I tried to test the sound, I got the message "The device is in use by another application."
 
Update: After restarting my computer, I was able to find the drivers in ASIO again. But the problem still remains whereby when I opened a browser / media player, the drivers immediately disappear. Is ASIO meant to be exclusive? I would think they should still allow us the option to share the applications - especially since I've already chosen that. This is quite undesirable for me as I do need to listen to music while working on SONAR at the same time.
 
Please do advise, many thanks in advance.

If browser and other media apps aren't sharing the driver, there's not much to be done in SONAR to resolve that other than ensuring that SONAR is always launched first and set to share drivers, and that its sample rate and bit depth are the same as what the other apps want.
 
Personally, I prefer to avoid the whole issue by leaving the onboard PC sound system active, and setting it as the Default Device for playback and recording in Windows for use by browsers and generic mutimedia apps so that they keep their mitts off my MOTU which is dedicated to SONAR and any other apps I specifically configure to use it.
 
I have an outboard mixer that allows me to monitor the PC sound output through my studio monitors.

Thanks for the response.
 
1) I guess an outboard mixer will mean an additional hardware purchase? I am guessing a cable with an audio jack (to connect to PC sound card) and into an "in" port of the audio interface..
 
2) How do I ensure that the sound driver is being shared by all? I've already unchecked on my playback/recording to enable it being used as exclusive. I also checked SONAR to share drivers. But that didn't solve the problem once SONAR is turned on. 
I tried launching SONAR first, before opening the other apps, but once I did a media playback, the drivers in SONAR disappear. How do I check the sample rate and bit depth of my browser and media player?

Something like a Mackie Mix5 or used/refurbed 402-VLZ4 would do the trick without breaking the bank.
 
You don't need to run the output of the onboard sound back into the Tascam, just route it in parallel to your monitors along with the output from the Tascam using 4 input channels of the mixer. In my case, I use the Tape input to the mixer because they're RCA connectors, and 1/8" stereo-to-dual-RCA cables are common.
 
Since I really don't do the driver-sharing thing with generic multimedia apps, I'm not really in a good positon to give detailed troubleshooting guidance. It may be an issue with that specific driver.

Ok, after purchasing an audio interface and an outboard mixer, all seems good now. Seems a bit of an overkill for now considering I merely wanted to eliminate latency in my keyboard playing - but I'll never know if these will come in to greater use in the future.
 
Thanks for the help guys.