The two things to check then are to confirm that sessions are being accepted and created for your traffic. Setup the ping and then use:
show security flow session source-prefix 1.1.1.1 destination-prefix 2.2.2.2
This should show the accepted sessions with nat and packet counts. If there are no sessions you will need to enable trace options to find out why.
Second thing to confirm is that the remote side has the return route for the traffic and that they ahve polcies to accept the traffic as well.