You probably need to repair the links in External Data Sources (in File > Manage > menu).
As a further conversion stage, though, if the database is as simple as you say you should also consider importing the tables from each of the related files and consolidating the database in a single file.
Agreed! A clean fresh file rather than 3 polluted ones... which obviously don't take advantage of all the newer possibilities.
At the very least you should consolidate data sources so the relationships in each file all use just one.
Pre v7 files kept a record of everywhere those files have been... ever. When you opened them it would try the last one then if that fails the previous one etc etc. This all needs to be cleared out.
I would highly recommend running MetaDataMagic on the original files before conversion. It will clean up file references automatically possibly saving you a lot of work later on.