If it is an IDE or sata hard drive should be able to purchase a hard drive enclosure that will permit it to work as a external hard drive via a usb cable.
http://popular.ebay.com/ide-hard-drive-enclosure
Another alternative may be to take the hard drive and swap it for hard drive in the dell you just bought if it is the same type. When you reboot you should have access to enable you to back everything up. Should be easy enough to do your self. Most hard drives on dell are below a cover with two screws on the base. Remove the screws unplug the drive and plug the old one in, don't need to refit the cover. Restart in safe mode if it gives any errors.
Everything will be saved on your hard drive nothing will be on the memory Ram.
Give me a call if you need any help or bring the computer to me and I'll do it for you but it should be easy enough.