Can I transfer files from the hard drive of a non-working desktop computer to an external drive or another computer?

This can be done easily. I dont know how old your computer hard drive is or what operating system its for but take off the cover to your computer there should be a wire connector with a few wires going to your harddrive. Find a wire that is identical to the one going to your hard drive. Than look and find the wire that goes from the motherboard to your hard drive. See if there is an extra one of them inside. If not take the one from the old computer and use that. Just plug it into the new harddrive than into the motherboard(there should be a port somewhere near the other one). Than boot the computer. If a second hard drive doesn't appear in explorer its going to be a little harder. First go into device manager and see if the harddrive is even reconized. If it is it won't be that bad to fix. If it isn't something is wrong. Check all the wires again inside the computer and listen to see if you can hear the second hard drive running. IF it is spinning it is getting power! You than have to go into the bios menu and enable it!

This is easily done, you will need something like this: http://www.newegg.com/Product/Product.aspx?Item=N82E16812232002 OR IF it is compatible with new system set-up, simply set the old HD up as a slave to new HD (basically shows as a secondary HD) and either just use that HD too or drag and drop whatever files/programs you need to new HD. This is also what you will do if you use the USB adapter too