Site migration issue

I'm moving a site from one host to another, and followed these steps:

1. Copied all files from current server.
2. Did a mysql dump from current server.
3. Uploaded files to new server.
4. Created and imported database to new server.
5. Got a temp license to run aMember on a temporary domain

Now I'm having trouble logging in to the members area. I'll go through the login procedures, and it will redirect me back to the login area.

Feels like a cookies, or a sessions issue to me. Has anyone had this issue?

I can't figure out why it would work on one server, and not on a different, similarly equipped server.

Thanks,
Bryan