Ok, good. There are a few important things here:
- Intel Core 2 Duo T5850(2.16GHz) --- Good, just as long as it's Intel.
- 64 bit Dual Core Processor --- Good, Mavericks only runs in 64-Bit mode.
- Intel GMA X3100 --- Good, Intel integrated graphics.
- Intel High Definition Audio 2.0 --- Good, Intel audio.
- Windows Vista Home Basic --- Absolutely terrible, but doesn't affect anything.
So, to recap, your system should be compatible. I'm still working on the OS X Beta, so I'll report back.