Are you sure you have the correct SIMMs for this system? are the SIMM's you have the same brand, spec and I/O speed (2GB SIMMs). If not your SIMM's may indeed be the issue not the socket.
Mixing different sized SIMM's can be tricky as the smaller sized SIMM needs to be in a given slot. But before you go into adding this 4GB SIMM make sure its I/O speed and specs are correct for this system.
Review your models memory requirements from Apples Tech Note: http://support.apple.com/kb/HT1270
The first slot (slot 0) needs to hold the smaller SIMM if you mix sizes. Running different sizes forces the computer into a slower I/O method. If you use the same size (matched set) your system will use inter-leaved I/O which is much faster!
I would try a fresh set of matched SIMMs (2 or 4GB) to make sure your going down the right path here.
In any case using the wrong type and speed of SIMM or you have a mis-matched set can create sporadic operation and cause the reaction you are seeing.