I am having trouble mining ether and receiving ether in test-net. I have left my computer on to mine overnight, but still have 0 ether in the morning. In addition the transactions say that they went through but nothing appears in my account. Do you know what I am doing incorrectly and how this problem could be fixed?
UPDATE Ropsten testnet has been revival on March 25, 2017. Check here for more information.
The latest testnet called Ropsten is currently under severe spam attacks that leads to normal transactions unable to proceed. If you want to use the testnet for development, you can checkout an alternative testnet called Kovan, which is an effort to combat the spam by using PoA protocol.
Another option is to use testrpc.
The transaction you made was actually pending and waiting to be mined(or confirmed). There must be at least several confirmations to legitimate the transaction, sadly it's pretty hard on Ropsten due to the above reasons.