Everyone has given good advice, but the ultimate decision is probably going to depend on the total cost and real time before you plan to add a full second story. I have done dozens of roofs in my time and can give you the following considerations.
A new roof is probably going to cost you around $300 to $350 per square (10ftX10ft or each 100 square feet) for a complete strip, 6 feet of ice/water shield and new 30 yr shingles. Not knowing the size of your roof and pitch, I can't give you a real good guess, but a simple 24X30 cape with a chimney, no crickets or tricky valleys usually runs around 3 to 4 grand. Any good roofer is going to insist that any damaged or rotting roof shiething be replaced while it is stripped, adding more cost. Don't count on using the old roof structure when you remodel. Raising a roof under a new wall system can be very expensive and I suspect you have an original rafter system and board sheithing. Your new roof will want to be of the newest materials and techniques such as trusses, tounge and grove sheathing, soffit and ridge vents etc. A second story is a huge investment and in my humble opinion, very wise to do it all new.
As far as possible repairs to your old existing roof, you may be able to replace some shingles in the field easily, and repair the leaks around the chinmey with a good coat of blind nailing cement or even remove a couple of feet of shingles and treat the area with Grace ice and water shield then reshingle that small area. Obviously, we can't see or judge the general condition or continued life expectancy of the existing roof. I would strongly suggest you stop the water ASAP as Tester is right on saying a couple years of water can cause you a lot of other problems. Good Luck
Any moisture issues related to the standing water incident would have manifested itself long before now. Whatever the current issue is, it's unrelated to the previous issue. In that time, it is possible a new leak developed. It's also possible the dark areas are related to interior humidity and unrelated to the roof. In cold weather, the ceiling surface under rafters is measurably cooler than the nearby portion under insulation alone. This can cause condensation only under the rafters. As you know, condensation can lead to mold.
Can you tell if the darkening is due to actual mold? The damp surface can attract dirt that darkens the area even though no mold is growing. Even though the dirt can stain, attempting to clean an area with plain soap and water would yield a very different result than if mold is actively growing.
If mold is actively growing, it is time to consult with a mold professional. They will determine the cause, mitigate the mold, and suggest how to prevent it from happening again. If you want to investigate further before going that route, the only reliable way to determine if the rafters are getting wet is direct inspection.
Cut a small inspection hole where you think it's the worst. If it's wet up there, a lot more ceiling is coming off, so don't bother patching the hole. The roof is leaking. It needs to be repaired and all wet drywall and insulation needs to be replaced. If it's all dry, breathe a sigh of relief. The need to patch the hole is much less than it could have been. Be sure to adequately seal the damaged vapor barrier.
If the rafters are dry, the only thing you can do to reduce condensation on the ceiling is reduce the overall humidity of the house. First try selective ventilation and lifestyle adjustments. Consider bumping the thermostat up a bit. If that's not enough, look into continuous ventilation through an air to air heat exchanger.
A far as replacing stringers, that cannot be done with comp roofing unless a full cold roof is installed. It is normal practice for concealed structural spaces filled with insulation to not be ventilated. It sounds like the roofers followed conventional building practice.
Best Answer
It is possible to replace individual shingles when some become missing but there are factors to consider before deciding to replace the whole roof covering.