It's quite possible that you were mining with a mining pool, in which case the pool may still be holding on to your bitcoins for you. In that case, all you'd need to do would be to figure out what your userID and/or password are for the pool. If you can find/remember the pool name, they might even be able to look up your usereID for you and allow you to reset your password.
Some of the more popular mining pools back in 2011 were:
- Slush Pool (the first mining pool, introduced in late 2010 as Bitcoin Pooled Mining Server)
- BitFury (also known as pool.io)
- BitMinter
- Eligius (also known as Luke-Jr's pool)
- btcmp (also known as "bitcoin minepool" or, occasionally, as "stratum")
Do any of those sound familiar to you?
There may be a few others, but those are the ones that come to mind for me.