OK.
First, it should be possible to get a Realtek on-motherboard sound chip working with Sonar. On-board sound chips can generally handle playback, but will be far from ideal, especially if you meed to record audio or play a software synthesiser in Sonar using a MIDI controller, but you say you don't need to do that.
ASIO drivers provide, amongst other things, a very low level of delay between playing a note on a controller and it emerging from a software synthesiser, amongst other things. Again, you say you don't need to do that so don't worry about it at the moment, let's just get sound working. In any case, there are no ASIO drivers for Realtek that I'm aware of, amd the freeware ASIO4ALL driver which can sometimes be persuaded to work with Realtek is very hit and miss, difficult to configure and can itself cause all kinds of problems if present on the system.
So. First, go into Windows control panel/device manager and locate the AMD HDMI audio device. Right click on it and disable it (do not uninstall it, just disable it or Windows will spot it and re-install it automatically) Having graphics-card relayed HDMI drivers (which are mostly intended for playing hi-def video/audio on a home theatre system) active can confuse things.
Now make sure that there is nothing running that might use the sound card so that Sonar can have sole access to it. It's also a good idea to go into the control panel/sounds settings and tell Windows not to use any system sounds at all. That will (hopefully) prevent Windows from grabbing the sound card and denying access to Sonar or making unwanted noises at the wrong time.
Open Sonar go into Sonar's preferences and set the pull-down for audio driver to WDM or MME -
You should then see the realtek listed under audio devices. Select it as output and input device.
Now open a new project, call it 'test' or something similar. To check you've got audio working try dragging a wave (not mp3) file into the project and playing it back. If all is well and correctly routed you should now get sound.
To get MIDI playback in Sonar you need two things. One is a MIDI track containing the MIDI data and the other is an audio track with a software synthesiser (such as TT100) in the fx bin. The output of the MIDI track should be set to point to the software synth and the output of the audio track should point to the master bus which in turn should be routed to the realtek.
Sonar is very powerful but has a bit of a steep initial learning curve. I strongly suggest you work through the help tutorials to do with the basics of getting things working, MIDI and software synths as these will take you through things a step at a time.