I knew the problem was with that damn .sparseimage file, and as I said, all I could figure out about it was that it had something to do with backing up space and with something called FileVault.
All I know about FileVault is that sometimes when I restart my computer, a message pops up recommending that I click "OK" to recover disk space that is not being used efficiently in my FileVault. When I was having the disk space problems just now, I purposely restarted in the hopes that I would get that message, because I suspected it had something to do with refreshing the information in my Finder.
And I was motherfuckin' right!
So after all of the DVD stuff had transferred onto my desktop, I deleted it from the laptop. It was 13.8 GB of space...and yet, even after I emptied my Trash folder, I had the same paltry amount of disk space available: 414 MB. That made ZERO sense. Mainly out of desperation and having no clue what else to do, I restarted my computer. Unlike with the previous restart, the FileVault message came up. I said OK, and after my computer had restarted, my Finder was displaying that I had a whopping 36+ GB of space available. Yay!
THAT makes complete sense, because all of the HP DVD stuff I had done was gone (either deleted or transferred onto the desktop computer and then deleted). In addition, I had cleaned out some small bits of crap that were lying around my hard drive...resulting in my having MORE space than when I had started out today.
Gosh, I feel like I've been typing in another language. It's so weird to be talking about FileVaults, MB, GB, etc. I really knew nothing about all this until just earlier today.
Anyway, so I'm happy that my laptop is healthy once again. And even though it is 1:30 am, I am not going to sleep. Instead, I shall try to import that one clip into iMovie on the desktop, so at least I can play around a bit with it before I turn in. I deserve that reward!
I still want a better way to do all this, though.