I don't think you can determine maximum age if you don't have the last ring.

You could determine minimum age by assuming the tree is circular and the rings are regular. For timber trees, this is a fair assumption, because they chose straight trunks for long, straight timber.

Edit: maybe a process like carbon dating could give you an age at death. Carbon-14 dating only works for stuff at least 500 years old or so, and for trees you still need the outer rings, so that specific process wouldn't be useful here.

The first step, in my opinion, is to find any existing local-ish datasets. I reckon that around you, there could be trees that go back well over 1000 years to use as a reference. You could then try to find the oldest ring of the wood in your house. It's probably pretty hard to count back before that, but you could try to make estimates based on the circular ark of the grain pattern to determine a trunk diameter.

You would want to send out a sample and have professionals reference their data. I guess you could try and get their data(maybe a university researcher would be favorable) and do the cross referencing yourself, but dear God that would be tedious.