1992 Chrysler New Yorker Over Heating

I can run my car for an hour, it doesn't go past 1/2 way mark on the temp. If I drive it for like 10-15 mins in town, it heats up super fast, at times it max's out, gauges start sounding and coming on. At this point its boiling over (out of the coolant reservoir). I recently replaced the Rad with an aluminum rad, replaced all hoses and lines, rad cap (16lbs), thermostat.

The rad fans don't come on at all, at any giving time. The rad relay I suspect to be no good. How can I go about finding out what is cause this overheating, while avoiding a heavy shop bill. How can I determine if its the Water pump, or a blown head gasket (it doesn't smoke, leak, or lack power in any way or form)?

Everything else on the car works in tip top shape (except the reverse lamp relay, both reverse lights are currently not working either, but I can handle that). The body Km's are 227,000, but the engine (and wiring) and transmission only have 87000 km's (replace happened at 140,000 km's on the odometer).

Any more info needed, let me know A.S.A.P.