Re: 03 Explorer starting issues
If the battery is original since 2003, chances are good its toast. When a battery begins to freeze the electrolyte is limited on performance, especially if the electrolyte in the battery is low. If it's not too low you can add a softwater and vinegar solution (50/50mix) to the battery. If the level is very low and 250mL isn't enough to bring it up, then get a new battery. If you're unsure how to check or add solution to the battery, don't. The coil may also be on its way out.
If he wants to leave it at the dealer or a reputable shop. I'd start with the electrical test, move on to fuel pressure test next and knowingly it's one of those. If it has 75K or more miles and hasn't had a tune up, get it.
'11 Ram Quad Cab 4x4 SXT 5.7L HEMI (stock); 48,500m
'06 Pontiac G6 GT 3.5L 220hp; 64,000m
'12 Chrysler 200 Limited 3.6L 283hp; 28,000m
'99 Taurus 3.0L 2V Vulcan 145hp; 154,300m - Traded
Amsoil in all vehicles!