If you're distributing the COM separately from the Access DB, then the COM cannot find the DB. By forcing the path to "c:\..." you're requiring the DB to be on the computer that the COM object is installed.
If you need to distribute it separately, you could setup a DSN on the computer hosting the Access DB, or put it on a shared drive that everyone has access to.
Under Win2k, you can setup a DSN by going to Start > Settings > Control Panel > Administrative Tools > Data Sources (ODBC)
Once you have a System DSN setup, your COM's Connection String would point to the server and DSN that's hosting the Access DB.
If you plan to have many people using this COM, and accessing this DB, concurrently, MS Access is not very robust. You may want to consider migrating the DB into SQL Server.