neildownx offers many words of wisdom, as always.
Could I suggest you go to your old PC and work out how much data you need to transfer. 10Mb, 100Mb, 10Gb or whatever?
If you don't have a lot of data you could use a USB memory stick. You can pick up a branded 4Gb memory stick for less than �20.
You copy data from the old PC to the memory stick. Transfer the memory stick to the new PC. Then transfer the files from the memory stick to the new PC. Delete the files from the memory stick. Repeat as necessary. 10Gb would take three goes to transfer all the files.
The memory stick can, of course, be used umpteen times. So although it costs you money, you can reuse it.
Of course, if you're happy with a screwdriver, take out the old hard drive and add it to your new PC. Note that it may invalidate any warranty on your new PC.