Mower has new battery, solenoid, starter replaced last year. When trying to start as soon as compression builds the engine stops and will not turn over. What do I check next. If I jump start The motor will run once it turns over a couple of times. I have also checked all electrical connections

Most likely you need to adjust the valves. There are some good videos on YouTube for "briggs single cylinder valve adjustment" I like the one from smalleng.com.

Hi,
And the link to that video is:
Lawn Mower Repair Valve Adjustment - YouTube (http://www.youtube.com/watch?v=NjzX-PUjKmo)
Peace,
Clarke