@ Zylark
welcome back to Amiga land:)
Obviously 1st thing is to remove that old leaky Ni-Cd battery and check for any damaged MB traces. You can find nice little coin type battery holders that will operate the clock without any worries (Amigakit sells them else you can find them at most electronic stores).
2nd I strongly recommend you replace all the MB caps and PSU caps as thats a very common problem in miggies today especially if its been sitting for a long time. As Mike mentioned check the PSU fan and make sure the fan is blowing to the rear of the PSU (pushing air out-search here as I know there's a recent thread about sizes, types) and since you're there I would highly recommend you repalce the PSU fan to reduce the noise and increase the CFM (trust me don't get lazy on this and do it & thank me later:rtfm:).
For the yellowing of the case, look up RetroBrite. It works.
Have fun restoring
ah found the psu fan thread here:
http://www.amiga.org/forums/showthread.php?t=55070&highlight=amiga+4000