From my experience with similar chipsets, no. Windows will have a fit about the different southbridges (ICH4 in the 2350, ICH5 in the 3000), most likely with a STOP 0x7B BSOD at bootup.
Depending on what CPU is in the 3000, a CPU swap may not work either. Certain versions of the 845-series northbridges don't work at all with Prescott CPUs (Celeron D, or Pentium 4 with 1 MB L2 cache).
As for Northwood support (plain Celeron, or Pentium 4 with 512K L2 cache), it'll likely run at a much lower speed than in the 3000. The 845GL only supports a 400 MHz front side bus, whereas the 865GV in the 3000 supports 400, 533, and 800 MHz FSB speeds. Any CPU that normally uses a higher-speed FSB will run at reduced speeds in the 2350. The 3000 likely has a CPU that normally uses a 533 or 800 MHz FSB.
Probably the easiest thing to do, if there's room for it in the case, is to add the other hard drive as a secondary. Personally, I'd do what koitsu
suggested and do a fresh install. Fresh OS installs make me happy
.