15 year old tires that have sat in the same place for the last 2 years could have a problem caused by flat spotting, unfortunately they probably won't be cost effective to try to have the tires shaved to make them round again. The 1st warning sign when old tires go bad is a new vibration, usually the belts in the tires are loosing the bond with the tire plies. The next notification is a sudden worsening of the vibration, just before tire failure. Often times the time frame between the 2nd warning and failure isn't very far apart, often measured in feet travelled. Been there, had the destroyed fender to prove it.

If it were me, I'd put new tires on the car. Gene