To my knowledge there is not any mechanical means by which a CD is detected in a CD player. It is all based off whether there is a reflection of the reading laser light onto the reading surface. So if there is a CD in it would sense the laser. There must be an isssue with the reading surface circuit or the laser itself in the CD player. Unfortunately it is a board level failure which means that you would spend much more money trying to fix it rather than replacing it.
So, you should look into an aftermarket replaceent. If you aren't replacing speakers or adding an amp replacing the head unit is not too hard. You would be buying the CD player, and adapter for the trim and an adapter for the wiring harness which. The wiring harness adapter is a simple instal with just a couple of saudered wires to the new CD player you can plug it right into the stock wiring harness and you then only need to add the new trim adapetr.
It is an hour to do the job and there is plenty of support for any installation. Try www. Crutchfield. Com as they are a weel known retailer and have good selection, prices and excellent customer support. Don't be intimidated by the installation. You can do a much better job of installling it yourself rather than paying someone who is trying to install it as faast as possible and will end up doing a sloppy job.
The adapters make installation easy and are available for any application.