Nissan Repair: 1996 maxima not starting in cold weather, air fuel mixture, cold cranking amps

Question
I have 1996 maxima good condition only has small hole in exhaust from cat to front engine , under 100,000 miles.....now that its cold sometimes it will not start so my brother suggest that I hold the key in its on position and accelerate the gas and this did work but I feel tis will damage something ...what could be the problem I had a pre-inspection and everything is good and the only thing that needs to be repaired is the hole in the exhaust

Answer
it sounds like a tps issue if you need to adjust your throttle manually on a fuel injected car to get proper air/fuel mixture upon startup.   could also be a bad battery not producing enough cold cranking amps as well.  take you car to a different mechanic to get a better lookover, obviously you have an issue and that shop didn't really care.