Originally Posted by cciman
Detail strip and clean out the the firing pin channel, and the clean the striker safety, extractor components.
Check the contents of the striker pin channel while doing so: you might as well take out and check the sleeve when doing so to make sure it is not falling apart or broken (search the forums on how to do this-- i think I posted some tips for removing without damage), look at the tip of the striker.
You might want to replace the striker spring with a Wolf Xtra power striker spring to improve reliability.
Yes the trigger bar should be contacting (riding over) the safety plunger.
I suspect you've gotten a Glock that was previously owned by one of those guys who thinks Glocks never need to be detail stripped or cleaned properly. They do. The safety plunger can also get so gummed up with crud that it may be stuck as well (in the upward position), which would make the gun very unsafe even if it was firing. Until it's cleaned right, you won't know what you've really got going on.