Regardless of where the billboard company built their sign, it would still be construed as their sign. The bigger issue is the rent that went unpaid for maybe decades to the prior owner, and may now be your money (that's definitely a technical, legal issue). In most states, there is case law on "trespassing rental income". For example, if you went onto a neighbor's farm and rented an abandoned house on the farm for $500 per month for a year, you would owe the farmer $6,000 in rent, because you "stole" his rental income. To me, that's the case here.
My bet is that the billboard company thought that it had a handle on where the lessor's lands boundaries were, but didn't bother to do a survey. That's not the first time it's happened. I don't think they have a legal leg to stand on, so I would definitely hire a good attorney and see what you can do with the situation. If they threaten to take the sign down, then you can file an injunction until they pay you all the rent you are owed -- which might be a huge number (the gross rent on the sign for the number of years it has been there). However, if the lawyer tells you that you have no legal ownership of that old "rent" then you may instead elect just to strike a new, fair lease with the billboard company and be happy that you had such a luck out.