It says 4/unconfirmed.
Recipient computer shows 0 connections 60,000 blocks (approx) and 0 transactions.
Can you lose these things for good?
That would suck ... I went pretty heavy
0 connections...there is your problem.
Block count needs to be at least 130665 for your transaction to show (current as of this posting)
The transaction looks safe, the receiving computer doesn't need to be on or connected for the transaction to go through. It went through when it was confirmed by a miner. For maximum safety, generate one or two new addresses in the receiving side, then backup wallet.dat from your AppData\Bitcoin directory onto a USB flash drive.