Of course it can be done. It may be easy or difficult, depending not on the control panel you had before but on the underlying software of the system you used before.
It will most likely need to be done at the shell level of the machine you used before. Many systems have a script called "formail" (not the same as formmail; note the spelling) which can break up an mbox style mailbox and reforward the emails in it to a new location. For some system (specifically those running the Maildir directories, i.e., those using qmail), you'll need to convert the Maildir directories into mbox format first.
If you don't have the skills to do it yourself hiring someone to do it for you could get expensive, depending on how many mailboxes are involved.
Do you still have access to your old machine? If so, then you should probalby just set up an A record in DNS pointing (for example):
oldmail.example.com IN A old.ip.num.ber
and having your clients log into the old box to get their email.
Jeff
