Well, for starters, from what I've found on the Net, 256 Meg of RAM IS the Max that this HP Pavilion 6730 will take.
Then, until if and when the specific problem is found as to what's causing this intermittent problem, it wouldn't be a good idea to waste money on more RAM if the problem gets worse and I eventually have to finally retire the computer.
For example, there in the beginning of the year, I had already bought a TigerDirect.com Gift Card so as to buy a CPU Fan from their website. At first I just simply procrastinated ordering the Fan. But, then the problems started cropping up. I then went, "Okay. I'd better hold off on ordering that CPU Fan cuz if this computer bites the dust, I will have wasted $12.00 for a CPU Fan that I won't be able to use."
So yeah, for now I''m holding off on that CPU Fan until I see which direction this mystery is going to take.