both HD and time machine (external HD) corrupt

Recently, my Imac (early 2009 vintage running Maverick) wouldn't boot, and all I got was the grey screen, with the sort of task bar looking thing which would fill and then the machine would shut down. After troubleshooting for an eternity, I came to the conclusion that the hard drive needed to be completely formatted and software reloaded, etc. I have been backing up continuously to an external drive using Time Machine. In the process of my troubleshooting, I tried to restore from the backup, and the machine wouldn't even recognize the external drive, so I started worrying about the integrity of my backup. So I bought a new hard drive, swapped it out, and installed a fresh operating system. When I attached my computer to the "backup" external disk, again, it acted like it couldn't even recognise the disk. I let it sit for a few hours, and finally, a window popped up saying that the disk could not be repaired, and I should backup whatever I could and reformat. I have yet to put the old internal HD into an enclosure and try connecting as an external drive to see what can be salvaged.

It would appear that something (virus?) hosed my internal drive, and had its way with the backup drive as well. Anyone else experience this? Any other theories? Any advice on recovering files from either the old internal drive or the "backup" drive?

thanks in advance!