Question: My dell 8400 tower went down, replaced power supply and ..nothing. How can I get everything off the hard drive, install into another tower, or take it somewhere to download to external drive?
Answer: From what you've described, it sounds like your motherboard is probably fried. Since the Dell 8400 series run an old Pentium 4 processor, it's probably not worth bothering with trying to replace the motherboard and you're better off trying to get the data off the hard drive and replace the system altogether.
You have a couple options for doing this. You can hook up the hard drive as a slave drive in your new system, or you can use an IDE adapter that plugs into a USB port and treats your hard drive like an external USB drive.
Either way you'll need to remove the hard drive from your old system, which is easy to do. Remove the screws from the outer casing (some cases let you slide the side off without removing screws) and locate the hard drive. There will be a flat thin cable about 2 inches wide connecting it to the motherboard. Remove the screws holding the hard drive to your case (usually 2 on each side) and then remove all cables and power cords going into the hard drive.
The easiest way to get data from your old hard drive onto another desktop system or laptop is to connect it using an IDE adapter. The adapter will connect your hard drive with your other system's USB port, and will let you copy files over just like it was a USB flash drive.