If a computer tower got knocked over while it was working, then stopped working, is it completely dead?

Possibly, but unlikely. Most likely a cable/ram/power/video card connection has come loose. Open case and ONE at a time REMOVE and replace any connections from hard drive, cd/dvd, ram remove and replace. Be sure pc is unplugged first. Secondly, touch power supply box inside computer first, before anything else.

It is most likely not dead completely.

When it tipped over, most likely some of the components were knocked loose. Most likely it would be one of the PCI or video cards that are installed inside the computer.

All you need to do is open the side panel of the case while the computer is off, Dell cases can be tricky. Then simply make sure all the cards are securely in their slots, the cables are all still plugged in and everything is seated properly.

Then try it again.

If something came loose then you're lucky.

I'm betting the hard drive is destroyed. It's not able to sustain a shock like that while it's spinning...

Did you check inside the case to see if a power cord came loose?

it usually isn't completely dead, but something could have touch the motherboard causing a shock which fried some components of your computer. you should have each and every part checked out before you go buying yourself a new computer though.