If your basement has a furnace/mechanical room, the trans was often there.
Is the old fusebox a 4 fuse box, in that case there are only a few original circuits... vintage homes were designed to have one light and one outlet per room. Often the entire lighting/outlet was run on one fuse. Anyway, try killing all the power except the doorbell:
"Cut as many circuits as you can off and walk around the area where you think the transformer is with an AM radio (tuned to a blank channel) and listen for the buzzing to change tones. The transformer has to be powered up though."
I'm betting on either a furnace room or it being covered in the remodel (which is against code and a fire hazard ).
Edit: Sometimes the trans was installed inside a box behind the doorbell.
Is the old fusebox a 4 fuse box, in that case there are only a few original circuits... vintage homes were designed to have one light and one outlet per room. Often the entire lighting/outlet was run on one fuse. Anyway, try killing all the power except the doorbell:
"Cut as many circuits as you can off and walk around the area where you think the transformer is with an AM radio (tuned to a blank channel) and listen for the buzzing to change tones. The transformer has to be powered up though."
I'm betting on either a furnace room or it being covered in the remodel (which is against code and a fire hazard ).
Edit: Sometimes the trans was installed inside a box behind the doorbell.