[J1mmy]

The ways in computers are connected to the router (wired or wireless) doesn't affect whether or not they can share files between one another.

The first thing I would check it whether they are both on the same network. You can do this by right-clicking on my computer, going under 'Computer Name' and checking what workgroup each of the computers is on. You would also come here to change the workgroup name, if they were not the same.

Since you have established an internet connection for both computers using the router, I'm not suspecting any DNS/IP error at the moment.