Spiders can't get in...there's a mesh screen in the inlet side. I realize your situation here, but taking plugs out is not going to help.
Your gas valve is likely bad. The coils were a good start and usually a cheap fix, but it has become apparent that the valve has issues, most likely bad springs in the plunger & diaphragm assembly. Any time something useful sits idle for long periods, atrophy will occur. It is the same with humans, only harder to fix
If your mom and pop outfit can't get you the 306176 valve, I can. Most of the others don't have the time to do the customs forms, etc associated with a simple transaction. You can read up on my policies here