Thought I'd follow-up on this. I surprised myself and was able to fix my laptop. I wouldn't say it was an "easy" fix. Maybe I underestimate people, but out of 10 average people, I suspect 1 or 2 could probably do it successfully from start to finish ... on average. It's not rocket science obviously, but I have an edge with my Electrical Engineering and Computer background.
It took a heck of a while to get it apart and it took a heck of a while to solder the supply off and back on. In fact, I lucked out and someone in our lab offered to do it for me because he recently had the same problem. It took him a while with a microscope, solder tape, and all the gear. It would have taken me hours longer I suspect even with the same equipment as I haven't soldered in a while.
Anyway, I put it back together and it booted right up and the power supply lights up no problem now.
I just put in an order @ ibuypower dot com for this desktop:
AMD Phenom™ II X4 945 Quad-Core CPU
Microsoft Windows 7 Professional
4 GB [2 GB X2] DDR3-1333 Memory Module
NVIDIA GeForce GT 430 - 1GB
Primary Hard Drive - 64 GB ADATA S501 V2 SATA-III SSD @ Read: 355MB/s ; Write: 75MB/s
Secondary Data Drive - 1 TB HARD DRIVE -- 64M Cache, 7200 RPM, 6.0Gb/s
[12X Blu-Ray] Pioneer BLU-RAY Re-Writer, DVD±R/±RW Burner Combo
12-In-1 Internal Flash Media Card Reader/Writer
MOTHER BOARD: Gigabyte GA-870A-UD3 -- AMD 870 w/ 2x PCI-E 2.0 x16 USB 3.0, S-ATA 3.0 RAID
SOUND CARD: Creative Labs Sound Blaster Audigy SE
Mid-Tower Case (Height:16" ~ 21") with Cold Cathode Neon Light
Liquid CPU Cooling System [AMD]
500 Watt Power Supply
My current desktop is so slow I can't even play music while I play poker because when HEM is importing hand histories, it steals too many resources. Hopefully now I can play poker, listen to music, and use applications I haven't been able to run before like Table Ninja and Table Scanner. It should be cooler than the other side of the pillow ...