Troubleshooting Toshiba Satellite M35X-S149

I've posted this at a couple other sites, but I'm looking for a consensus of opinions, so I'd like to see what everyone here thinks as well.

I have a Toshiba Satellite M35X-S149 that is having some issues. I'd appreciate opinions about what fix to try first, as I'm on the fence about what the problem really is.

Background:
Purchased new, only owner, purchased December 2004. I did have to have a warranty repair performed a few monts after I purchased it due to the system locking hard and displaying gibberish on the screen. I also had to replace the power inverter about 4 months ago. Other than that, it has always worked very well. At least, it did, until about 4 weeks ago.

I went to boot it up one day, and it wouldn't. I'd get the blue ring, the green LEDs on the front, and the fan would spin up, but it wouldn't boot. However, if I reached around the back of the unit and wiggled the AC power cord, it would boot up and then work just fine. Ever since, I had to wiggle the power cord to get it to boot or come out of sleep/standby.

Well, Friday night I was using the laptop, and out of the blue it just shut down. I am unable to boot it back up, even if I wiggle the power cord. When I hit the power button, I get the blue ring, the HD activity light burns for about a second, the fan spins up and then stops, and the LEDs on the front burn. That's it, it does nothing else, it is literally silent.

I have tried removing and reseating the memory modules. I have tried to boot it without the HD, and tried to boot it without the battery. Nothing works.

I know that these Satellites are notorious for having problems with both the power jack and the motherboard. The fact that I was able to, for awhile, wiggle the power jack and bring it to life, has me leaning towards purchasing a new power jack and installing that to see if it works. I haven't tried putting pressure on the mobo when I try to start it, as I just read about that on the web this morning and the laptop is at home (I've read that if this works that's indicative of a problem with the Maxim chip on the mobo).

I'd like to get opinions from other people about what is causing my problems, because I'm hoping to only have to crack it open once.

Thanks in advance for the replies.