Did a back up copy, the savefiles are corrupted and I (kinda) can't save my progress

[Braylovsky]

English ain't my first language, sorry if you see some engrish.

I don't know if somebody experienced what the title says (since I couldn't find any info), that is why the new thread.

To keep things short: my laptop started acting sketchy, and just in case I made a backup/security copy in an external hard drive. One thing let to another, and now I can't use my old laptop anymore. I started using this new laptop, and tried to play again a game I left unfinished, but the save was corrupted. I checked the save file, and I found that, aside from the folders, all files in the external hard drive had a date and time just next to their name (the moment all of them were backed up). I renamed them (just removed the date and time from the name) and the game recognized the save file, I could play again, but now I have troubles saving my progress. Just to give some examples:

• Dissidia 012 says "Memory stick is full. Check your storage space (80110383)". I can't overwrite my savefile, just make another one. Since the game saves automatically often, I see this message often.
• Patapon 2 and Naruto Shippuden Ultimate Ninja Impact do mostly the same as Dissidia 012, but without the initial message.
• Valkyria Chronicles ll works fine the first time the game saves, but from the second time onwards it says "Other savedata already exists. Save to the storage media anyway?". From what I have tested, it's like a gamble, because sometimes the progress does save, sometimes it doesn't.
• Valkyria Chronicles 3 is mostly the same as ll (first time it works, second time onwards it's random); the message says "Media Storage has changed. Do you wish to save to this new Media Storage?".
  

I don't know how to fix this. The examples I just gave are all different (3 games are US region, 1 game is Europe and 1 from Japan; 3 are .iso files and 2 are .cso files).
I guess I can keep playing, either by constantly create new save files or only save once if I feel playing risky.

I don't know if this has a very simple solution and I am stupid, or this is a very specific issue and I am less stupid. And yes, the save files are in the correct path (PSP > SAVEDATA > ULUS/UCES/NPJH > Files with correct names).