I got a new PS3 and I was trying to re-download LittleBigPlanet from my downloads list but I wasn't able to find it. I then searched for it and purchased it thinking it was going to be free considering that I already got it before. Is there any way I can get my $28 back?
If you were logged in with the same account & password you used to purchase the game originally then the game would have been available to you.
Searching on the store would have resulted in you finding the game & being charged for it exactly like you did, why you thought it would be free I'm not sure!
It's unlikely you'll get a refund because the error was your own fault but it's worth a try, you will have to contact Sony customer service to request a refund, the number is below.
Mon - Sun 6:00AM - 10:00PM Pacific