Have a 91 blazer that would not start without a jump. Bought a brand new battery 2 days ago, started yesterday no problem this morning would not turn over. Lights and radio are on. Could it be something with the starter?

Absolutely,those starters will start making connections internally when worn out.There by draining your battery.Another thing is oil,if the starter starts soaking up the stuff the oil will make electrical connections all by itself.Try cleaning it with brake clean or starter fluid,probably take a couple cans to get it clean but it might work.Now this stuff is highly volatile and not good to breathe so you'll need good ventilation.The area should be free of cleaners before start up (FIRE!),this will give you plenty of time for charging up the battery.This is a temporary fix,repair the leaking valve cover and replace the starter before it melts down completely.Good luck!