*Disclaimer* This is a different model MBP than my own. It may be a COMPLETELY different issue. This is just my experience with what seems to be a similar problem.
Hey man. I had/have a similar problem with my a1260 mbp 15" (with so much surgery performed on it its basically like Joan Rivers. Major parts replace once, graphics card recall, entire top half replace...all different incidences). It became so bad (a little bit after the top half and a memory upgrade to 6gb) with the sudden shutoffs that I couldn't boot it up anymore. Battery in, battery out, charger in, positioned vertically, at an angle (read on for that fun bit), being very gentle with the CPU load...you get the idea.
However, before it became that bad, I noticed something odd. If I kept the laptop propped up by putting something that was about the thickness of two fingers put together at about the battery area, it would stay on (sometimes).
Now the bad news. The ability to change the behavior with changing the position made me think it was a short or a contact issue. I did some poking around and noticed that certain pressures on the power button of the top-case would cause the shutoff. Again, sometimes, and the pressure was not always necessary. It was some kind of short I believe. However, after running a stress macro, the problem showed its ugly head again. I tried going back to 2gb ram. I tried a number of things. Every time, the same issue.
I said "frack it" and brought it into someone a bit more knowledgeable than I, my local repair shop. They opened it up and almost immediately suggested that it was the left i/o board, citing that it may be an issue with the way power is distributed from the battery/charger. They replaced it, sealed the laptop up and ran into the issue. They then called and asked if I wanted to replace the I/O board in my (going on) 5 year old MBP, an $800+ repair in a machine that-while it has served me faithfully for those five years-has required WAY more than I purchased it for in repairs.
I'm now wondering if I can scrounge the board from another MBP somewhere in the world/my local sphere, live with the problem, or...perhaps buy a new laptop. Perhaps one that isn't so crazy expensive to repair or replace parts. I only hope that laptop supports Lion. :(
So here's the long and short of it Chris. The problem became so bad I would only hear the boot noise and then it would shutdown. A replacement top-case (ie the part with the speaker-holes) fixed the problem...sorta. I haven't spent any real time with it since that fix, I basically turned it on, used it for a couple of days intermittently (I have an iMac and another MBP that I had pretty much switched over to when this problem became unmanageable in october), suffered the problem again and took it in. I'm not sure if the total fix is replacement of the Logic Board, but the repair shop certainly thinks so.
Sorry buddy. But look at it this way. My laptop is from 2008, yours 2007 if I'm right. They're old man. It really sucks, but it may be time for us to replace our laptops.