If you need to copy only small file(s) use a flash drive - plug it in, copy the file(s) to it, unplug, plug it in in the second PC and copy the file(s) to your new hard drive. If you don’t have a flash drive you can use your digital camera or mp3 player exactly the same way (unless they are very odd or old model).

If you need to copy a lot of information then you should consider networking the two computers:

Using direct cable connection - you can use crossover cable to connect the two PCs (they both must have network adapters), for more info click the link below:
http://support.microsoft.com/kb/305621

If you have a router and want to learn how to set a network between the two PCs read this tutorial:
http://www.homenethelp.com/web/howto/net.asp