1988 Playskool Expres Train engine won't run. Light comes on but wheels won't turn. How can I repair it?

Check the wheel rubbers and track. In case if rubbers on the wheels of engine are deteriorated, it happens. Similarly if track is oily same happens. Try running engine only. If it moves, then add wagons one by one.

It is a vintage item and not much known about it.

https://www.google.com/search?q=Telco+Santa+express+train

Most repairs can be undertaken at a local model shop. If they don't do it, they will know someone that does.

..

I see you say 'calcification' Judy, so a white residue from a leaking battery? Scrape the white scale off with the point of a small paring knife. Then you can use a green pot scourer to remove the rest and make the metal shiny. An old typewriter eraser also works well, the sandy, gritty type, or even an emery board for the nails. Then clean with a damp cloth and then rub or with a little Vaseline. This will stop further corrosion. Then put the batteries in and try again.

https://www.google.com/search?q=Playskool+Express+toy+train

..

https://www.google.co.uk/search?q=vintage+Great+American+Express+train+set+manual&client=ubuntu&hs=jgI&tbm=isch&tbo=u&source=univ&sa=X&ved=2ahUKEwjgprLy7vLdAhViB8AKHRn8BwkQ7Al6BAgCEA8&biw=1853&bih=922

Once you identify the train set name.

Google vintage Great American Express train set <name>

Go to Lionel.com for a list of authorized service centers or order directly from Lionel.

I am assuming you are using the Lionel CW80 power source. If so, the blinking light might indicate a partial short or a problem with the motor. The reason I believe that is that the CW80 has an internal fuse, which will blow for near shorts/shorts. A stalled motor i.e stuck drive gear, can cause excessive power drain although not enough to blow the internal fuse and also cause the engine not to move. Also, If the engine has the neoprene belt on one of the drive wheels it might have come off and is jamming the running gear or wheel. I believe the Polar Express only has one neoprene belt.

CLEAN wheels, roller pickups & track.

if its like the peg perego one, the battey that runs the vehicle is under the seat, and the batteries that run the lights and sound are in the smoke stack

the sounds are run off of a different battery source, check the battery under the seat and make sure that its connected

Here are a couple of resources from New Bright:
http://www.newbright.com/public/electric-train-faq

http://www.newbright.com/images/Manuals/384%20ws%20manual.pdf

There is no On/Off switch on the train. Power goes from wall plug to transformer, then from transformer to track clip, which must be attached to the track. A control line goes from the track clip to the controller. Mine has a green light just above the red On/Off button that will come on even if the engine and tender are not on the track. The tender does all the work, and must be connected to the engine and on the track. There are four sliding contacts between the tender wheels that provide contact with the track.