I've worked a lot with older stuff, so I'll pitch in my knowledge.
The CPU you have a is 486 DX4-100 with a 33 MHz bus. The "DX4" was a marketing ploy - it only has a 3x multiplier. There is no 486 DX-100, all 100 MHz 486's had multipliers.
You could easily run Win95 or Win98 on there (haven't tried anything NT based). I've got a 486 DX2-80 system crunching away at SETI right now 🙂
On SETI, you'll probably run into about 250 hours per WU, if it's anything like my 486. All 486-type chips have unpipelined FPU's, which make them about half as fast as a Pentium at similar clock at floating point math. Integer preformance is similar to a Pentium.
I tried running Quake 3 on my 486 (64 MB ram, Voodoo Rush) - an average of 2 FPS. Not bad, eh? 🙂
You could load up that thing with memory, it's dirt cheap on eBay - look for "72 Pin FPM" memory.
EDIT: Forgot two things to mention.
The PCI slot is probably PCI Rev 2.0, which can have compatiiblity issues with newer cards. A safer bet would be an ISA NIC, although they'll be slower.
Conner was the previous name of the company we all know and love as Seagate.
That huge ISA card you have looks like an IDE controller / sound card / modem or NIC. / floppy controller. Good stuff!