Buy your new pc. Take out Drive on old Dell pc. attach via cable to usb on new pc. Browse to your files and copy to new pc. If necessary rightclick - properties, and take ownership of files (if you get Access Denied)
If possible on old pc make the files 'Public' so you will have easier access to them. ClickHere
use adapter Cable or caddy to attach Sata/IDE hard drive to usb port. Yours are probably Sata drives, have a look at the connection to make sure.