Have a furnace, compressor ok, can I install a heat pump

If both your central air handling fan and outdoor compressor are running and your not seeing any sort of cooling after a 10-20 minutes than I'd venture a guess and say it's time to call an AC repair service.

I'm curious what you are pushing in that makes the compressor turn on? Are you somehow bridging the main capacitor? Capacitors tend to be a common point of failure on AC units and can actually be changed fairly easily. Here is a pretty good article detailing the steps to do so.

To be honest though I'd guess that the bigger problem is the fact that you can get it running and it still isn't putting out cold air. The whole situation sounds like it's low on coolant (have you had it filled in the last few years?). AC's usually have a low coolant pressure switch that will keep the unit from running to prevent damage to the compressor when there isn't enough pressure.

Call an AC service out, many will diagnose your problem free of charge and be able to give you a much better idea of your problem. Be warned though, if your system is old and uses R-22 prices have shot up in the last year.

Try this on for size:

Annual Oil Bill * Efficiency = Cost of Oil actually used for heating. (The rest is waste).

So on an annual bill of $1000, you are currently paying $650 for heat, and $350 out the chimney. (i.e. $650 is as low as you can go with a 100% furnace)

So, if you were to replace that with an 87.2% furnace, your annual cost would be $650/87.1% = $747, and there is about $100 waste. (Note! this is a savings of $250 per $1000 of Oil)

On the 86.1%, that's $650/86.1% = $755 for a difference of $8 per thousand of oil currently used. At that rate, the new furnace would take 375 * (time in which you use $1000 of oil) to pay off the difference.

This analysis is based purely on BTUs produced at the burner.

Now, there are other factors, such as air flow and distribution which may significantly affect your oil use, and the bigger furnace may be more efficient in other ways.