With a laptop you do not have a lot of hardware debugging choices. But I would try this:
1. Take one of the memory Dimms out and run it on just one Dimm. If it is still on the blink, try the other Dimm. If it runs OK, you know it is the memory Dimm in question and can change that.
2. Burn a Linux CD - e.g.
Puppy because it is small. Run that from the CD reader (change the BIOS boot sequence). If that works well, you know it is a Windows problem and we can dig further.
You can also run step 2 before step 1 if that is more convenient. If none of those steps shed any light on the problem, we'll have to regroup. There can be many other causes.