Lionel PCB E-Unit Diagnostics

I was going to say replace the board, $35 including shipping from Lionel, but it's not available. You could order some smoke wicks, too.

No, matter how you repair it, I would put a polyswitch in series with the track power(hot) wire to prevent future frying. Sorry about that, I can't find one that will work.

I would be concerned about the cause of frying.

The board is only 5 wires to solder.

So, go for the transistor replacement and search for a board in case other components were fried. Check the switch and wiring connections.

I'd stick the transistor in first, it may have simply gotten overloaded due to a motor stall and died.  The PTC isn't a bad idea, one of the 1.5-2.0 amp trip models would probably be a good choice.

I almost forgot, Welcome to the forum!

Here's a 2.2A Polyfuse, probably not a bad choice.

If the new transistor you put in eventually burns up also then I would suspect that the heat of operation is what is killing it.  Heat is a killer of silicon electronics.  I am guessing that the bad transistor handles the current drive for the motor in the forward direction.  So if heat is the problem, I would expect it to fail again in the future.

If you had to do a second repair, I would try to fix the heating issue also.

While I had the engine apart I would look for any way to add a heatsink to that transistor or both transistors.  Those transistors look like TO-220 body style so they should have a screw hole under that tape on the top.  Usually that metal top of the transistor is connected to the center lead of the TO-220 transistor.  I would look at the space available inside the engine and try to mold a piece of solid copper that could screw to that transistor.  However you fit it in, you would want to keep it insulated from other metal surfaces including the transistor next to it.  For solid copper you can cut up a piece of copper plumbing joint or tubing and hammer/cut it into shape.  In the photo it looks like there is insulating tape on the tops of those transistors so I would guess that the two transistor tops are not in common electrically.  At $0.60 I would buy 2 or 3 of those transistors for backups.

If the problem continues, I would find a suitable location on the inside of the engine body that I could mount the transistor to using an electrical insulator and then wire the transistor back to the circuit board.  The electronics supplier should have insulators for that TO-220 transistor also.  It is a material that is thermally conductive but not electrically conductive.  The surface you mount it to should be smooth and flat with no pointy, jagged surfaces that can puncture the insulator.  The more airflow or larger mass of metal the better it would work. 

Good idea with the heatsink, wish I had thought to mention it first.

You can use the insulating mica insulating "washers" cut for the TO-220 package to mount the heatsink across both transistors, more area, better heatsinking.  You'll need the nylon insulating shoulder washer as well.  Also, I favor a thicker piece of material, usually aluminum as I have it and it's easy to work.