First thing you should do is clean the old computer. You don't want the infestation to spread to your new machine.
Use an antivirus like, avira. avira.com
Anti spyware tools use:
ad-aware from lavasoft.com
spybot search and destroy. safer-networking.org
Download these on your uninfested computer and copy the installers onto a usb stick, or burn them onto a cd. Load your old Dell into save mode (pressing F8 at windows startup), install the programs and let them run and clean the system (one at a time). This will take several hours to do, so just let them finish and after that you can start thinking about copying files over.
You can use windows7 easy transfer wizard to help you find stuff that is important http://windows.microsoft.com/en-US/windows7/products/features/windows-easy-transfer
edit: If all else fails, you can buy a external usb harddrive cable like this one http://www.microcenter.com/single_product_results.phtml?product_id=0285941.
Then just uninstall the harddrive from your old laptop and plug it into your new one. From there you can then clean the drive and get the data you want to rescue.