I bought some bitcoins on LocalBitcoins then downloaded Bitcoin-qt then instantly sent it to my wallet and now the wallet is corrupted... Is there a way to get them back?
Create a backup of your current wallet.dat file. Check this is you don't know where the file is stored.
Check debug.log in your bitcoin datadir, see if there are any errors, ask somebody, post here, post on IRC
Start bitcoind or Bitcoin-Qt with command line argument
-salvagewallet(if you don't know how to run a Application with command line arguments, try to ask someone or get help over IRC freenode/#bitcoin.
If step 3 didn't help, check if you have a backup from your wallet.dat, replace files (only overwrite your wallet.dat if you followed step 1).
If nothing worked out, get help from a bitcoin expert over IRC (but never give away your wallet.dat!)