I had the same problem with my Kenmore Elite HE3 gas dryer. Went through the troubleshooting guide and the solenoids tested fine. However, after more research I chose to replace them. Here's the link to the ones I installed:
https://www.amazon.com/gp/product/B072Z98M2S/ref=ppx_yo_dt_b_asin_title_o00_s00?ie=UTF8&psc=1
It's a ten minute fix, take off the toe panel after shutting off the gas and electricity. There are two philips head screws that hold the solenoids in place. You'll need a stubby screwdriver to get them off because there's not much room to work. The slide out easily and have keying holes to align them correctly.
Remember to shopvac the inside of lint while the toe panel is off and to clean the vent pipe.
Dryer is back in action and working. Good luck!