Bricks, Masonry, Asphalt and Concrete - Should I tear down Chimney or repoint older bricks????

I recently purchased a 1920s colonial. The chimney is being used as a vent for the oil burning furnace and the gas hot water heater. My problem is that the base of the chimney is deteriorating badly, some bricks are almost completly gone, others turning to dust....I bought the house knowing this and want to either take the chimey down and reroute another vent for the furnace and heater or keep existing chimney. The chimney is enclosed by walls thru the 1st and 2nd floors and in the attic the previous owner covered the bricks with mortar all around it...I can only see the attic and basement portions, the basement portion looks bad and the attic portion is completely covered...Should I just remove the chimney since I cannot see between floors or should I try and repoint the bricks in the basement??? Also don't know if chimney is a supporting structure in the attic..

Get a opinion from a reputable HVAC contractor about installing stainless or aluminum pipe from basement, and eliminating existing chimney, it sounds like it about to fall, or get opinion from bricklaying contractor.