Time to play detective with my grandma's old PC.

Alright so, I have a bit of a problem. While I was over at my grandmothers house for thanksgiving, she pulled me aside and asked if I could take a look at her computer. Needless to say, it was total crap (I'll brief on specs later). After a quick analysis of what I was up against, I realized that it would need to be taken home to be worked on. I assumed that it was just some malware and toolbars that I would have to clean up.... But I was very wrong.
After a clean install of Windows 7 Pro (yes, a legal copy), things started to get weird. I started getting visual tearing on my monitor from a vga output directly from the motherboard. Along with this, the computer would also turn itself off without warning (kind of like having a bad PSU). So, I went to fry's and picked up a $40 Enermax Case and a Nvidia Geforce 8400 GS. My idea was that a GPU might stamp out any rendering issues, and it did. However, the random shutdowns became more persistent. I tooled around with different operating systems on the build (Arch Linux and Puppy Linux) but the shutdowns continued.
Today I picked up a 430w Thermaltake PSU, and the problem just got worse. As soon as the windows login is prompted, the PC shuts off. However, I am able to boot windows 7 in safe mode with zero issues.
I am at a loss as to what to do, because I need this computer fixed without putting too much more money into it. I'll throw the specs and extra points below.

~ Before I made any changes to pc ~
-HP Tower, circa 2006(?)
-233w HP PSU
-crap asus socket AM2 board
-Athlon 64 @ 2GHz
-4 gigs DDR2 RAM
-500gb seagate HDD
-No gpu
-standard cd drive

~ After I made changes to pc ~
-Enermax Tower
-430w Thermaltake PSU
-crap asus socket AM2 board
-Athlon 64 @ 2GHz
-4 gigs DDR2 RAM
-120 gigs Samsung 840 Evo SSD
-Geforce 8400 GS
-standard cd drive

~ Points to note ~
- I am sure it is not heat related, temps are fine and my case cooling is near perfect.
- I have 4 fans. 1 in PSU, 1 inflow on front, 1 outflow on back, one on cpu.
- Front fan is powered my fan header on board, back fan is powered by Molex connector.
- I have tried 2 different SSDs and an old HDD, didnt work.
- I am going crazy.

Please guys, I am begging you for help. I dont have the money to buy my grandmother a new computer, no matter how much I want to. I am open to any suggestions and help. Thanx.