Code 35 is exactly for the solenoid, most likely it does not work anymore. You can on the other hand get a new one from Carquest like I did, its about $50. Or you can just leave it and drive as is, it doesn't affect the running of the engine.
You could test the Resistance and see what it shows, I'm not sure how much resistance it should have, anyone else know?
Also, like Cookie1 said, there are two of them. One is for the EGR, and the other is for the 4WD, you will notice the vac line on the other runs down to the trans mission (At least on the 3AT)
Cheers.