Using Windows 7 on a Lenovo desktop with Firewire. All Firewire and Alesis drivers are current and up to date.  Windows device manager says all drivers are functioning properly.  Upon booting Sonar the Alesis Multimix is recoganized  and is set for WDM.  All channels input and output show up in the "preferences" settings.  I have tried changing the bit rate, the sampling rate, disabling Windows sounds, disabling the integrated sound card, and changing firewire cables.   Secondly I installed the same hardware and software on a 2nd computer and got the same result.
 
Does anyone out there in Sonar/Alesis recording land have any suggestions?

I've had good luck with the ASIO drivers of the Multimix 16 F/W for a few years now. Currently using it with Sonar platinum on W7.  Haven't tried WDM for a while. Was not good in prior driver versions.
 
Is your Alesis firmware up to date?
Can Windows use the Alesis (in WDM)?
 
Some firewire controllers are said not to work well with the hardware in the Alesis (and similar TC & Presonus units). Some f/w interface chips from LSI, TI, and Agere are compatible. Some from NEC and JMicron are not compatible, according to this list. So have a look at your firewire device properties on your Lenovo.

If you are running ASIO4ALL uninstall it immediately.
Update to the latest firmware and drivers for you audio interface. Use ASIO preferably in Sonar.
If that does not work try deleting AUD.INI (google for details).