As far as shops go, you would be surprised at how little skill most places have for finding hardware issues in a computer box. I wouldn't trust any of them half as much as I trust the guys that post in this forum. Basically what they do is try and turn on your computer and if it doesn't cut on they name some hardware components off the top of their head and say that is what is broken. They usually name two or three components, that way if you ask them to repair it, they are covered for their time and investment in parts to fix the computer. Unless hardware components are tested one or two at a time, usually nobody will know what is really broken. Last time I had your problem it was something as simple as a bad cpu fan. Fortunately I have have lots of parts so I replaced that and all was good.
As far as dell goes I wouldn't trust them either. I mean maybe they are correct and the card will not work, but maybe whoever told you that is somebody they have to answer correspondence and not a real live hardware geek know it all.
I have been exactly where you are now and this is how I first got interested in computer hardware and how to fix computers. If you want to fiddle with it and feel qualified, here are a few steps. Proceed at your own risk, not mine.
Try reversing everything you have done so far to see if you can get back to square one. Take out the vid card and install your old card, or if you were using on board video use that. Put the same psu you were using before back in. Basically, try and get back to what you had going the last time the system worked. If this does not work the next thing to do is to get the computer to start with as few components as possible.
I can't really remember so google it, but I think you need a mobo, a psu, a processor and a processor fan to cut the computer on and see if power is running threw everything. I think?? Then if it does that see if you can get to the bios. I don't know, but maybe you will have to add at least one ram stick to get to the bios. The idea here basically is to add components as few at a time as possible until you get to the point your monitor will light or untill you get to the point you notice something odd that happens which will be a clue as to what particular part is broken. It helps to have extra parts to switch and swap. and if you don't have these, then all may be in vain testing this way. Maybe you got another computer or a friend who has a broken computer with some parts????? I got some of my parts from computers I found laying out for the trash man to take.
My gut is telling me your mobo or processor took a hike for some reason or another, maybe????? but I bet your hard drive is fine at least. Good luck.