Dirty contacts can certainly lead to a malfunctioning camera so should clean the contacts.
However, IMHO, if it was only a lens contact problem it is unlikely that the camera will switch on after reinserting the battery - so if cleaning the contacts doesn't work, try using a different battery.
5D3, 6D, 600D, RX100
16-35L, 24-70L II, 70-200L II, 100-400L, 50L, 85L II, 135L, 24TSE, 40, 100 macro, 18-55 II, 55-250 II, 600RT x 4
I come here to learn something new, not to learn how bad my gear is - I know that already ;-)!