Hi and welcome to LQ,
If you don't have much experience in dns, it could be a bit painful. But you should upgrade at least for security reasons.
Looking at your OS (RH 6.2), I guess that your server is running bind 4.x. You have to verify it's running bind and not some other dns software, otherwise what follows is of no use.
There is a
migration guide from version 4 to version 9, but I suggest you to do the following:
Install your preferred OS and use its bind package. Then edit by hand named.conf to add the zones your server is authoritative for (you can use the named-bootconf.sh from the link above, to have an idea how they should look like).
Then add the zone files in the appropriate directory (copy them from the old server and make sure they follow the example in the link above).
Lastly run named-checkconf to check named.conf and named-checkzone to check the zone files.
Regards