Does the machine still work?
My first guess is that you may have fried the power supply, or possibly one of your cards (or something else). Sometimes it’s just a part that’s had enough, though you’re more likely to be looking at a power surge. Sniff around the back of the case, where the plug comes in from the wall, for more burnt-plastic smells.
Most desktops can be opened with a screwdriver and some perseverance; if you’re confident (and won’t be voiding anything by doing so), crack the case and examine the components for scorch marks. Unplug the machine and touch something metal (in order to discharge any static you might be carrying) before digging into the guts.
Dell cases are especially user-friendly, not even needing a screwdriver. Tampering with them might disqualify you from any Dell-based aftermarket service.
Try not to touch anything while you’re in there.
Computers are modular by design; so long as damage isn’t sustained to the drives or the motherboard, you – or the guy at the shop – can swap out the bad bits.