In this situation, invariably the Non Ferrous parts of the Heating system are ok, it's the Ferrous Parts, and particularly Steel Radiators that are prone to the worst effects of corrosion. Pointless just treating the symptoms each time, you need to sort the cause, which as Harry has said, is a lack of Inhibitor.
Basically heating systems are a nice mix of metals, Steel radiators, cast iron Boiler, a few yards of copper pipe linking them up and some brass valves chucked in for good measure. Then we fill them whole lot with water that then starts a nice electrolytic reaction within the system, and begins eating away at the steel Radiators from the inside out, creating Hydrogen gas and black magnetite sludge as a by product, which proceeds to clog up your system.
One bottle of suitable Inhibitor neutralises the water and prevents all this from happening, but so many systems are still operating without again, either it was never added at the start or the system has been drained down for repairs and/or maintenance, and refilled without the inhibitor being replenished.
I don't think you need an entire new system but some considered repairs to the existing will be needed. Any rusty Radiators, look to replace. Whole system would probably benefit from a Powerflush. This is where an aggressive cleaning chemical is added, before water is pumped around the system at high velocity, breaking up and washing out the accumulated black sludge. System, once clean is refilled and the all important Inhibitor added. Any new Boiler must be fitted to a clean system, otherwise the Warranty will be invalidated very quickly, but even if not going down that road, it can extend the life and increase the performance of the existing setup.
At this point I would be inclined to get the system Powerflushed and a Magnetic Filter installed to capture any further crud that may be floating about. If 3 Way Valve is faulty, replace. However lack of Hot Water may be an issue with a blocked cylinder coil, how old and how well insulated is the Cylinder? Your Boiler may well give many more years of service provided it is looked after properly.