I downloaded the demo of Lumines, to try it out. Today, I went to BestBuy to pickup the physical copy of the game. (I prefer having a shelved copy + box rather than a digital download.) When I inserted the cartridge, the install screen automatically popped up, after about 3 seconds, it froze. Restarted the system about 2-3 times, only for it to freeze at the same spot. I used the "Restore PS Vita System" option. This fixed it, I have all of my saved games and my PS Vita works fine, with everything installed. However, I lost all of my trophies for Uncharted, despite having sync'd them with the server on numerous occasions. The trophies from other games updated just fine, all except for Uncharted. Anyone else experience this? This is really disheartening.
Many things that require an install generally freeze at certain points for a while. Next time you need to be a bit more patient. Unless it was an hour long wait, then you had no real reason to perform a system restore.
Also, 3 seconds in and you couldn't wait? no offence, but you must be new to these types of things right? next time feel free to open up a thread for technical stuff and there will most likely be somebody to help you.
Trophies are saved on your PSN account, not your system. When you do a sync, all of your trophies will re-appear.
Edit: Looked back up and read it was only for uncharted. Try re-inseting Uncharted and doing an action which would cause you to get a trophy. I opnce clearned game data for a game which for some reason erased all the trophies off my system for it. I re-played the game and got 1 trophy, then synced and they all returned. (The game was Heavy Rain)