PS warning light came on while engine running, I cut switch off, cranked up & light didn't come on then!

If its one of the warning lamps not for check engine, then look it up in the owners manual and see what it means could be low tire air pressure or blown light bulb but if it is check engine light may not be anything real bad some come on when its time for oil change or may also be a code stored too, if it comes back on stop at a auto-zone and let them put a code reader on it to see code, they may know what it means or you may need to look it up and before replacing parts check all reason for it to set and test first. Otherwise check fuses and all fluid levels and electrical connections good & tight and do any maintenance scheduled per the owners manual.

want to the store came back ps light on car won't start but lights come on.

May have to have a shop or someone with a code reader/remover remove the code for you. May not crank because of safety feature, If it continues to come back on have the Power Steering System inspected.