Switch and push button ignition

The problem could be a few possible things, but I don't think your switch is the problem unless the switch is always left on.
But the first thing to check would be your alternator, carefully disconnect your neg. Cable from battery while it is running if the engine dies within about 2-3 seconds its you alternator, if it keeps running then, turn you car off. It is usually 1 of 2 things, the battery or the terminals are corroded, make sure you connecters are clean so a good metal to metal connection is made, on both termanals. If they where dirty or green or not on tight, give that a try, if that still does not work. Check your battery, take it to Checker or Autozone to test it, it is a free service.
If nothing I suggested worked, I am clueless at this point. Good Luck!