It all depends on the motherboard in your PC. That is the be-all and end-all of limitations.

You cannot take any old CPU and slap it in any motherboard.

If you change motherboard, you may have to change memory and/or graphics card too.

You basically need to find out if the motherboard in the PC supports dual core CPUs, then work from there.

If you can tell me the Dell Service Tag (Sticker on PC) I can probably tell you this info.