Macbook hangs when power cable unplugged or plugged in

My 2008 alum. body macbook, which has worked perfectly in nearly every respect, has been freezing up whenever I plug in or unplug the power cable. It doesn't freeze completely; usually the mouse will still move around, and sometimes I can even switch between open applications, but none of them will actually do anything. It also takes a very long time to start up (both on battery and cable power) and the battery life is significantly reduced. It has exhibited no other issues beyond this after a recent crash.

The computer froze up so I did a hard shutdown, and it wouldn't restart. I eventually got it to safe boot, and then restarted it. It now works perfectly, except for the hanging issue. I have tried a different battery (I put in my old battery, which worked fine other than having a very short charge life) but the issue persisted. As noted, since the crash and beginning of the problem, the macbook lasts noticeably less time on battery power alone. Should I try a new battery and see if that solves the problem? Would love a solution that doesn't cost $129, and really as long as I keep it plugged in all the time, it works perfectly.

If you tried a different battery and the issue still remains, this isn't likely a battery issue. Part of this could be the fact that you're running a 5-6 year old machine. I had an early 2008 MB that was rough around the edges in terms of performance and this was a few iterations of OS X previous to Mavericks (I think it was running Lion). The battery was also in very rough shape as would be expected of a machine of that age.

Have you done any maintenance on the machine? Have you run something like OnyX to clear up any old and lingering content that might be slowing things down?

I haven't run OnyX, though I will. I do maintenance and tried a Mavericks reinstall (though I didn't wipe the machine) when this all happened.

It had occurred to me that the computer is just old, but this problem happened so suddenly, after a crash, and there are no other performance issues with the machine - other than the fact that it did star to run a little more slowly after I installed Mavericks... which actually went away after a few days. So I'm thinking it's likely a hardware issue that occurred when the computer crashed, possibly something overheated. (Logic board, damaged RAM?)