Your best bet is to transfer the domains to another registrar, one that you know will be around for a while.... or to the actual company that issued your registrar their resellers permit. You will need to contact their customer support directly and let them know under what circumstances you are attempting the transfer. More than likely you will need to fax them photocopies your identification card(s) to verify yourself.

Years ago, I registered my domain names using an email address that I no longer had access to. Network Solutions wanted email verification at that time in order to process a contact information change. It took them about four weeks for them to process my new email address, but they wanted me to fax them all the pertinent info to get the ball rolling.

Today's customer service from registrars is much improved, so you probably won't have as much of a nightmare situation as I did. The issues obviously are different, but the processes to remedy them are similar.