I am trying to find out if a cap is bad or would cause a A/C blower the keep running at half speed once the heater shuts off.

Once the motor has started up and is running, the capacitor plays no part. Are you sure it's not a 2 speed furnace? Many furnaces cut back the speed when the flame goes out. The only purpose to keep running is to cool the exchanger so it doesn't heat load and cycle on and off.

Also check your thermostat for a small switch marked AUTO/ON, which setting is it in?

The thermostate is in auto, the only reason I bring up the cap is while searching for the problem I found only one answer and it talked about replacing the cap. The problem is that once the system shuts off the blower keeps running at a very low speed, pushing cold air into the house.

A capacitor stores power to get your blower running from a dead stop up to speed. I am fairly certain it has nothing to do with your issue. You could have a bad stat or a more significant issue with the furnace mother board or circuit board. Honestly, I would not worry if you still get heat at the right time and your home is warm. I turn all my stats to ON and leave them that way until I move out. Uses just afraction more electrcity and makes the home comfortable. Is you home being heated to the setting on the stat, if so just try to ignore this issue.

Thanks for the help, The house stays warm, but because of the blower staying on it is pushing cold air into the house causing the heater to cycle a lot more.

While you may think it "causing the heater to cycle a lot more" it really is not. Your home needs a certain BTU to keep warm and the blower running 24/7 does not alter the BTUs needed. If you stand in front of a register the air may feel cool but testing the temps all over a room and down at the floor and up at the ceiling you'd find its much more even than ever before. Moving air touching your skins always feels cooler than it really is.

While you may think it "causing the heater to cycle a lot more" it really is not. Your home needs a certain BTU to keep warm and the blower running 24/7 does not alter the BTUs needed.<snip>

That is correct unless you have poorly insulated ductwork in uninsulated or unconditioned spaces (attic, basement). Then you loose heat through the duct walls to the cold space. Same goes for cooling season except that basements are rarely hot.

Another thing to check: Some furnaces have a switch on or near the control board to keep the fan running on low with no call for heat or cool. Could that have been changed recently?

Never noticed a switch like that on the control board, have to look. I do see them on 99.9% of all stats

The circuit board does not have a switch but the stat does have a slide switch behind the panel, it says from left to right "C SW3 F" it is set on sw3 right now.

A bad capacitor can cause a motor to run slow. Most furnace motor capacitors are RUN caps, not START caps. Although they do help get the motor started, they also play a part in how the motors run once they are already going.
I personally have seen motors run at about half speed due to a bad run capacitor.
However, a bad cap will not make the motor stay running at any speed.

Thanks for the help, do you think the thermostat would have anything to do with it? Other than the fan auto run switch is put to run but that would cause the blower to run at full speed. Nothing inside the system shows damage but that dosen't mean a whole lot. Thanks again for your help.

This may help Motor run capacitor test chart (http://toad.net/~jsmeenen/capacitor.html)

Hey ballengerb1. Great link. Id be curious to try that.
They do make actuall cap tester, but good accurate ones are spendy. I use a multi meter that actually has a uf setting just for testing run capacitors(no good for start capacitors) and it is extremely accurate, but also a bit pricey. Of course when your testing these sorts of things on a regular basis, expensive tools are just part of the trade. However, for those folks at home that have the time and know how, the lightbulb test sounds like a heck of a good deal. Thanks for sharing.

I'm probably showing my age(70), hopefully not my ignorance, but I grew up with capacitor start motors, not capacitor run motors. At least up through the 70's many motors were capacitor start.

Correct you are ma0641. Many motors still use start capacitors instead of run capacitors. Also many large compressors. However, most residential motors for heating and cooling now use only run capacitors. I do mostly residential work, therefor don't even have a start capacitor testing unit. When I run across a start capacitor, I just take it to a local electrical shop and have them test it for me. But heck, the way things change these days, everything I post on AMHD today, will most likely be outdated in ten years or less.