You could purchase an external hard drive, ask a friend with an older computer if you can use it to load your files to a temporary folder and then copy across to the external hard drive.
Alternatively is the hard drive on your old computer definitely dead. Recently my old laptop died and I was able to remove the hard drive from the laptop, put it into a hard drive caddy (cost about £15 from pc world), and plug it in via USB cable to my new laptop and copy files across.