The first thing I thought was starter solenoid...that's how it acted...then the clutch safety switch...I'm going to check that wire hanging down to see what's going on..
That all said I've checked out small jump boxes and this one looks like the one I'm buying because it comes with a small air pump too....it has really good reviews ..
Rugged Geek Portable Booster Pack Emergency Jump Starter and Power Supply with LCD Display (RG1000 Safety Plus w/ Air Compressor)
Amazon.com: Rugged Geek Portable Booster Pack Emergency Jump Starter and Power Supply with LCD Display (RG1000 Safety Plus w/ Air Compressor): Automotive
Don't bother looking for a lower price I did and every site has the same price listed..