It's a bit hard to offer specific advice without knowing the details of what happened.
When you say "my computer crashed", there can be many, many reasons starting with a flaky power supply, logical file system corruption, dying hard drive etc...
If the hard drive died (or reported SMART failures, or made strange noises, etc...) you can definitely have unrecoverable data loss/corruption on those files. In that case, recovering from a known good backup is always the best option. There could be some loss still if the problem was unnoticed for a while and some corrupt files were backed up.
If there was a "logical" (as opposed to the "physical" problem described above) - for example after a power supply glitch and an OS crash - backups are still the best option, but data recovery might help. Note that it is likely to take a relatively long time to examine a full hard drive completely, much longer than a more simple "unerase" application.
I don't quite get what you did after that? Did you try to copy files from the old drive to the new computer? If that is the case, I would recommend again restoring cleanly from your backup.
If the problem occurred while restoring from one of the backup drive, and if you are experiencing the same issue on different files from the other backup drive, the issue could be a flaky USB/Firewire connection. I would at least check the cables and eventually try other ports if that is how you recovered your backup.
And yes, it is a good idea to check a few of those apparently damaged TIFFs with something like Irfanview, which is more tolerant to minor file format inconsistencies than Photoshop. Photoshop will complain loudly if files are too long, even if they are perfectly valid. Files that are too long are frequent after data-recovery or disk scans and fixes because files sizes are often rounded to the next allocation unit (example: a file whose size is 16386 bytes can be stored in three 8192 bytes allocation units, with the last one containing only 2 bytes: Irfanview and many other viewers will accept 24576 bytes as a file length and simply ignore the extra data, Photoshop will reject the file). If that works, you can probably script that over your 100 files for minimal time loss.
Note: in some important data-recovery cases, fixing a single files can take several hours, if possible at all. Make that days to reverse engineer the addressing scheme of some flash chips and/or SSD drives. I know this is a world of instant satisfaction and where everyone expects that everything works instantly and perfectly every time, but those crash/backup/restore/raid rebuilds/corrupted files situations are never one click instant things. We tend to forget that, just as we complain when a call placed from Argentina with an 80 grams trinket costing $29 doesn't go through to Hong Kong in 10 seconds...