Slow start and check engine turns on?

My car has never started as quickly as I would like but it has gotten worse lately. The 'check engine light" has started to go on (now) with key-on position. If I turn it to 'start', the engine turns over for quite a long time, until the light goes off-then starts right up. Can't figure out if it is fuel or electric. Thankfully, I have a new battery, but don't want the starter to overwork as it is now. Any thoughts.

One other thing. On my heater/AC system, 'air' only comes out of the 'defrost' outlets! What's up with that?