Data recovered but HDD corrupt, how delete files before sending to HP?

My HP Pavilion's HDD is under warranty & I have to send in the old drive. I want to delete sensitive text and data files. I mounted the drive as external to another Win7 laptop and used TestDisk to recover partitions and then recover my data, which I've already safely copied. TestDisk says that my System and Recovery partitions have bad MFT and MFT Mirror that can't be fixed. So I doubt I can access the files at all if I put the HDD back in the notebook, with a bad file system.

I want to delete the old user files in the C: partition and use CCleaner to write the space over with 0's and 1's. But Win7 in my new laptop can't "see" the C: drive - it shows 2 partitions on the external (Recovery & HP Tools), but 2 don't show up -- System and C: are hidden in a general "F:" disk. I can't access the drive/partition from Win7. I don't know why Recovery partition shows when it has corrupt MFT and C: won't show when it has good MFT.

The files can be individually listed within TestDisk application and a partition can be wiped but I don't want to screw up my warranty so need to just delete folders and files and then clean up. How can I do that?
Thanks.
(C and E are the new laptop; local disk F is the part of the external corrupt HDD that is not accessible but contains that HDD's System and C: partitions and G and H are on the external as well)

Thanks to both of you, BUT, from another forum post here, it seems wiping the disk completely may void my warranty. HP has my credit card # and could then charge me for the new HDD they sent. So I want to selectively DELETE rather than wipe.

Unless I misunderstood you, you already seem to have the choice of wiping select partitions rather than the entire disk - so you should be fine just wiping everything except the recovery partition. I don't think there would be a warranty issue with that.

Still, it's probably a good idea to call HP first as whs suggests.

I will try. I did call them and the particular rep I got said anything to do with the drive as an external was outside what they would discuss because outside of warranty coverage as a notebook drive. I'll try this specific question. They of course gave me the party line that it will be securely destroyed.

I just completed a Live Chat with HP and was given green light to wipe the drive :) and I have it in writing.