Car won't start.
Check to see if the connections for positive and negative cables are tight at the battery! I've found more non-starting problems directly related to that than actual dead batteries.
I'd remove each of the cables (one at a time) and clean the terminal and the post, then replace the terminal onto the post and make sure that the terminals are snug. Try to wiggle it with your hand after you've attached it.
Start checking the electrolyte levels (hardly likely with a new battery but who knows) if your battery isn't of the "sealed" variety.
Good Luck! BTW, what type of car is this? (W124; w201; W126 etc.)
Scotts Valley, CA.
1993 300 CE Cabriolet (A124) 131K miles
1997 C-280 133K miles
2000 BMW R1100RT 69K miles
1989 300 E 216K miles (sold)