Sounds like #1.
But yes, the data is gone either way. The "corrupted" video files are filled with either garbage, all 0s, or a repeat of the data from the first part of the card.
Basically this:
Card is only 4GB (say) but reports 16GB.
The "file allocation table" (which records the name and size of a file along with where on the storage its data is recorded) is at the start of the drive, so any device (PC/camera) will be able to add new files which appear to be in the non-existent extra 12GB of the drive, because they can be added to the file table fine (because it's always at the start).
However when the device tries to actually write the file data, it has to destroy some - the card is only 4GB. It will either silently destroy the data for existing files (overwrite), or for the new file (discard). From your description it sounds like you have the "discard" type.
The destroyed data is not recoverable - it physically no longer exists.
When you go to copy the file off the card, your PC will create a file that matches the size in the file table, and then tries to read the data for it. Because the data doesn't exist, the card "makes something up"... So the file is the right size, but it doesn't have the right data in. It's not "corrupt" as such - the data is not damaged, it's garbage - there's nothing of your original data there to recover.
Sorry.