How to back up all files INCLUDING Program Files?

I have a Windows laptop that's become sluggish and infected with malware and crap. I want to back up everything, format and reinstall Windows since I have crap saved every place you could imagine. I just got a 3TB external HDD and I've been attempting to back stuff up but whenever I try to copy it, it simply doesn't copy. Any full-proof ideas? Also: This will be a seperate forum post but if you have any info that would help, I would appreciate it. There's a virus on another hdd I'm backing up and AVG detected it when I tried transferring it to my computer, and then to the external hard drive? Any ideas how to prevent it from crawling over to other computers (will it even do that?)? Partitioning? Anything.

You can remove nearly any virus from any HDD using Hiren’s BootCD.

You can use again Hiren's BootCD utils for backup and restore. Create an image of the laptop's HDD using Acronis Backup, and then you can restore only Program Files folder, or any folder that you need from the image file.