Assuming I found the correct machine, the Windows 7 Dell Optipex 745 I use is similar in specs to your 320.
As you "loop" your audio via a mixer there will be no problems running B.U.T.T. and the PlayIt Live streamer at the same time. Just select the Soundblaster as a source to both programs.
I had trouble finding a Windows 7 sound card driver for the built in hardware on my Optiplex and ended up forcing the XP driver to install.
I use 32 bit Windows 7 with 4GB of RAM (which results in 2.99GB usable). PlayIt Live takes about 20%-25% CPU and that's all I have running.
As a bit of a test, you could feed the built in sound card input with a second mixer output and use that as a stream source for PlayIt Live and the Sound Blaster to B.U.T.T. and run them in parallel.
From my experience, on a LAN at least, PlayIt Live is extremely stable including the streaming plug in.
I have a couple of test setups which I run for experimental purposes to (in this case Icecast) servers based on Raspberry Pi's. Assuming I don't let Windows updates happen, the Windows 10 machine will run for weeks.
The Windows 7 machine has a slightly dodgy sound card driver so will typically only go for a few days.
For what it's worth, I've had loads of driver problems with sound cards and Windows 10.
I might look there first.
If you have a mixer then you could also run a second streaming program (B.U.T.T for example) for comparison.
I've also had the trial version of Rocket Broadcaster running and that is good. If I were running a 24x7 "public" service I might look at the paid version of that on a dedicated machine or B.U.T.T. on an old Mac.
For completeness, I also have "Dark Ice" running on one of the Raspberry Pi's and that has been running for 2 weeks without interruption.
I followed the excellent instructions at: