Unplug and remove battery. Hold the power button for 30 sec. Remove and reinstall both memory modules.
Try powering up again - that may solve the problem.
if it does not, try each module by itself in each slot until you isolate the bad module (which will fail in both slots) or the bad slot (in which case one slot will fail with each module). If the module is bad, replace it with a new one.
If the slot is bad, it's the mainboard that will need replacement. That may not be a terminal condition if you can replace the board yourself, but if you have to buy a replacement board and pay for the labor to install it, the total cost will likely exceed the value of the system. In that case, putting the couple of hundred dollars toward a new system will make more sense.