Chances are, if you performed a complete factory reset of your computer from the factory partition on your hard drive, then it's likely that you're good to go.
What some may have been suggesting is likely involving some particularly resourceful pieces of malware that would require a comprehensive low level format using something like
http://www.killdisk.com/
Which would entail an end to end writing of random ones and zeros and would involve all partitions including any factory restore partitions.
The short answer to your question is..... I have no idea what you are calling a "backup discs i got with my computer", so my answer would be a very tentative yes, with fingers crossed, because generally Windows 7 Installation Media, is not commonly called "backup discs", but may be, I guess.
The critical thing you need is the Windows 7 Product key for your installation.
Installation media for virtually any flavor can be acquired from here
Link Removed
So the media is not an issue.
Personally, I'd hold off pulling the trigger on a low level format until I was pretty sure that it was absolutely warranted.