The tire pressure warning light has been on in my car for about a week. The dashboard computer says that the tire pressure in the front right tire is 17 psi, but when I use the pressure gauge, the reading is almost 40 psi. Is this something I should be concerned about? What could be causing this problem?
Just for giggles…check ALL the tires. Make sure they are all in spec.
40 seems awfully high. What is the recommended pressure?
Your PT Cruiser has tire pressure sensors? What make/model vehicle is this?
The sensor needs to be replaced. It doesn’t read correctly, your car thinks the tire is low and the light comes on. They don’t last forever. Your local tire store should be able to hook you up with a replacement sensor for maybe $100. Or you can put a piece of black tape over the light and check them yourself.
They don't last forever.
I’ve NEVER replaced them…05 4runner with over 270k miles and wifes 07 lexus with over 170k miles.
Okay, some of them DO last forever. The one in the OP’s tire apparently didn’t! 
Is there a sensor in the spare? 40 psi sounds high. Check psi on door jam. I bet it should be around 32psi.
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The sensors have batteries in them. That allows them to broadcast the pressure signal. At some point they will indeed stop working as the batteries will not last forever.
Mike, I’m glad your 10 year old ones are still working but they are on borrowed time. 
I’m assuming this car has in-tire pressure monitor gadgets, and doesn’t use the wheel speed sensors for this function. Good idea above to check the pressure in all the tires, including the spare. If they all measure ok, one of the sensors has failed. Note that it is possible the sensor that failed isn’t in the tire you think it is. On some cars if the wheels are switched around, the sensors have to be reprogrammed, otherwise they’ll show up in one location on the dash lights, when they are really in another. You need a shop or dealership with the type of scan tool that does this job. Ordinary scan tools often won’t be able to do it.
If this happened soon after installing new or remounting old tires, that probably contributed, as it can stress the sensor.
Most of the tire pressure sensors that I replace are on 2001-2004 vehicles, the battery finally goes dead in the sensor. I have never found one to display the wrong value, I think you are looking at the wrong tire. It is necessary to know what kind of vehicle this is for this discussion to understand the system used.
I think @GeorgeSanJose may have nailed it
And I’ve seen this numerous times. There are lots of lazy and/or uninformed mechanics who don’t reset the tpms system after a tire rotation
I wouldn’t be surprised if one of OP’s tires is in fact at 17psi
Might be the right rear, for example, if the tires were rotated without resetting the system
By the way, setting the pressure way too high can and does turn on a warning light . . . on some vehicles
“setting the pressure way too high can and does turn on a warning light”
does on my Forester. When I picked up the car new from the dealer, I drove 400 miles with the tires at 45 PSI before the light came on, on a very hot day. That is, the hot ambient temperature increased the pressure enough to trigger the light.
I always check tire pressures on new tires immediately after leaving the tire store. They’re almost always high.
I hypothesize that bead busters aren’t consciensious (sp?) about properly reducing and setting the pressure after seating the beads (which is done with higher pressure).
If you find that one of the other tires is actually at 17 PSI, you should consider replacing it. Driving on a tire that low in pressure can quickly cause internal damage.
I’m sorry. I drive a 2009 Chevrolet Malibu LT now. Forgot to mention that.
Have you already checked ALL of the tire pressures?
It is likely that your display does not match where the tires are located so you will need to check each tire. Some vehicle TPMS have the ability to locate the position of each sensor. Yours does not, the positions must be entered manually after rotating the tires. See pages 5-64 and 5-65 of your owners manual for the procedure.