I am not sure if you were trying to access the same database from both computers (dev and other) or if you were trying to run the system in the "other" computer without talking to the "dev" computer.

If you are trying to access the same database from both computers, then what you need to do is modify the connection in the "other" computer to look for MSDE in the "dev" computer. Once it has found MSDE you just need to specify the database name. You won't run into any path issues since you never talk to the physical file. You will always go through MSDE.

If you are trying to run the system in the "other" computer without depending on the "dev" computer, then you need to (1) install MSDE in the "other" computer and then (2) create you database again in this "other" computer. To create the database you cannot just copy the MDF file. You need to use "SQL Server techniques" like backup/restore, or detach/attach, or recreate the database with a script.