You need to attach the converter-agent logs.
The ESX host is attached to a SAN and the disk I'm trying to use has about 1.2TB left. The server that I'm moving is around 70GB total.
When I browse the Datastore, I can see the C: drive from the server I'm trying to convert, but not the E drive.
Ok. Then it seems to me like a network issue. It could be related to network settings. I could find few posts where users were having similar problems. Try going through these
http://communities.vmware.com/message/593801
http://communities.vmware.com/message/922117
http://communities.vmware.com/message/711388
Hopefully this will help.