I made a raw transaction that bitcoin-qt validated (returned the hash with sendrawtransaction) and (I think) broadcasted
The problem is that the miners don't include it
That transaction is quite standard and has 0.03 BTC for fee so I don't get why... Is it possible that bitcoin-qt validates a tx that miners don't accept? I think not because miners use bitcoind too, so the same rules should apply
Irrelevant note: it's on testnet
the most possible explanation is that you did not have enough connections at that moment, so your tx did not reach any miner.
restart your client, wait for it to connect to a few nodes and then redo the sendrawtransaction - eventually it should get mined.
if not, you can post it in here, and we can have a look.