why did you jumper W to Y?
doing this will make the aux heat strips and condenser run at the same time. in cooling mode this will run heat and cool together effectively running up your electric bill.

did you set up the heat pump/normal and gas/electric jumpers right on the thermostat?

are you sure youre only getting 5 volts across the coil on the contactor? (meter leads on both coil terminals)if this true and you have 24v coming into the unit at the terminals id guess you have a shorted control wire, a bad board (if it has one) or a tripped safety (high or low pressure) switch somewhere in it.

if you have 24 volts at the contactor coil, replace the contactor. around here contactors cost around 7 bucks.
id call a different tech.

I jumpered W to Y because the t-stat instruction manual said to. Also, according to the site http://www.hvacmechanic.com/tstatwiring.htm Y is 1st stage heating on a heat pump, and W is first stage heating and may require a jumper to Y on a heat pump.

We didn't have any problem with cooling bills or anything back when we needed cooling.

As for safety switches, that's what I was hoping the tech would look at.

I looked up your wiring diagram and it appears y and w need to be jumpered. im assuming this is because Y doesnt serve as first stage heat in heat pump mode like 99% of other thermostats do. im also assuming w isnt wired to the aux heat and only W2 is wired to aux heat.

normally on a heat pump stat Y is used to engergize the contactor in both heating and cooling modes and the O terminal switches the reversing valve accordingly.

i..e.. in cooling mode Y energizes bringing on the unit with O energized to switch the reversing valve to provide refrigerant flow for cooling.

in heating mode Y energizes bringing on the unit with O de-energized to provide reverse refigerant flow for heating.

your stat does need the jumper in order for W to bring on the unit in heating mode with W2 providing the signal for aux heat. the stats i usually work with have a W/W2 terminal that serves as first stage heat OR second stage depending on setup configuration or dip switch settings.

im assuming W is only jumpered at the stat and isnt connected to the aux heat. if so this could work.
I normally work with honeywell or totaline stats which are congfigurable without the need for jumpers.
your stat is kind of a cheapo but if it serves its purpose more power to ya hehe.

I'd (if i were you) call a different tech out and ask him to look at tracing the safeties.
I would try to explain how to trace the control circuits but that task is best left to a qualified professional.

good luck

Here is a link that might be useful: Ritetemp 8050C stat wiring

If I apply 24V across the contactor coil, should it activate? Because when I do that it just clicks once like it's trying but failing.