I read that if the transaction is not completed in 24 hours the bitcoins are returned to my wallet.
That is not how it works for Bitcoin clients.
I had 16 bitcoins in my wallet on the 16th before I sent the 13. I now have 3 coins in my wallet. Are the other 13 gone for good? Are they in bitcoin limbo? If they are gone what caused the problem to happen?
There could be a couple things happening. Know that bitcoin doesn't lose funds. Either they are spent or they are still available to you for spending (presuming you still have access to the wallet).
So possibly the transaction is not being relayed. Is this wallet.dat possibly from a backup and the coins chosen for the transaction were already spent?
One way to force a recheck in the database is to do a -rescan
$ bitcoin -rescan
Are you using a current client?