all bitcoin transactions are recorded in the blockchain, if you sent it on its way then it irrelevant if their client died or not
look your transaction up on
http://blockexplorer.com/It's not irrelevant if you've emailed them about it and received no response from them in 10+ days.
I accidentally duped a 10 BTC transaction to a merchant using mybitcoin.com and am yet to get any response from them (mybitcoin.com, not the merchant).