First off, if your video card wasn't working or was fried.. this would Not stop your computer from booting up, your monitor would merely not post.
As for your problem, if you were paying the technician to sort out a different problem.. and this has happened then it's his fault, and should sort it for you.
Sounds to be like an overheating problem, computers usually shut off when the processor gets to overheated, or the memory is damaged or not seated correctly.
Make sure your CPU is not overheating, and the heat sink and fan is seated correctly - making sure the CPU is completely covered by a heatsink, and that the fan is correctly powered, second of all check that your memory is in Dimm#1 /Dimm#2 as appropriate..
Test all your memory (using 1 piece at a time -booting up) in #Dimm1
Test your powersupply as your powersupply maybe faulty, you can do this by trying a different powersupply of equal or better Power in the pc thats giving you trouble, if your computer turns on.. you know it was your powersupply that was faulty - so you need to replace it, if it doesnt make a difference then you now know that it's either your CPU or motherboard.
The next parts are slightly more tricky as you need other similiar computers.. so try your CPU in a compatible motherboard which you know works..
If it doesnt work with ur CPU from the faulty pc, u know its the CPU - if it does work you then know its your motherboard.
*To Waffle:
*Puts on "Are You Stupid BOY!?" Face* - Says: Video Card? - A VIDEO CARD!? your a moderator boy! a video card would not "stop" the system booting up. lol! *goes jumps off cliff*