Thats one crappy laptop, there is a BSD derivative called
m0n0 which is the only Unix I have used that I think would work without too much effort on such limited hardware, maybe I'm wrong and there are others out there but this is the only one I have used that I think could do it.
Other than that I haven't tried to use any recent FreeBSD releases on old hardware but I think it might be possible to use FreeBSD on it, plus FreeBSD is probably the best Unix to learn on and has a great community.
Even then it wont be easy if your new to Unix, 80C's only had like 40mhz or something didn't they. I would try and sell that thing to an antique store, it's probably worth a bit by now
Good luck.
Ché Kristo