Usually, the Transformer for the Door Bell is 'in line' with the button. Start by removing the button to see if you can tell if the wires go DOWN or up. If they go up, you might want to look in the attic for the transformer. If they go DOWN (which is most likely the case), you have to go down the basement and line yourself up with where the button is outside. Once you've guestimated that 'location', there's a good chance the transformer is up in the finished ceiling in the basement. Look for an access panel or a way that you can look BETWEEN the joists that are in line w/the button.
Hopefully, you can access it. If you can't, I suggest you buy a completely new system that's wireless. It's probably less 'trouble' to install than it is to rip open the ceiling, do what you have to do, and then put it back as it was. BUT, BEFORE you leave the store, tell the Retailer that you're most 'concerned' that the system will work in the basement as WELL AS upstairs. In the case the system DOESN'T work well in the basement, you want to be able to return it W/O a restocking fee.
My best to ya and hope this helps.
Jay J -Moderator
PS: My transformer is about 8' from the basement wall IN LINE with the button on the front of the house. It's mounted on the floor joist under the sub-floor ...