Fix 1;
Were the terminals cleaned [wire brush!] upon putting in new battery? That's all it takes 9/10 times. I had this happen to me once, and recently a buddy on his '14 Taco. Cleaned terminals really well with wire brush, then once on, coat with dielectric grease [don't have to do this, but it's a good thing to do].
The factory puts a coating on most batteries that's not visible but just enough to not make enough contact to crank it over.
*remove cables [make sure they're away from the battery to not contact anything, put a grocery bag over them or something!], now clean the terminals one by one with a wire brush.
Fixed? No - move on;
Fix 2; check ALL of the fuses/relays. Why? If there's any chance you jumped it or installed the battery backwards, this would blow fuses. Check them all over. Like ALL OF THEM, under the engine bay, interior fuses, etc.
Fixed? No - move on;
Fix 3; Try starting the vehicle in neutral to see if it will even crank over. Disengage shift lock - do this on level ground....
Fixed? No - move on;
I guess at this point you're scratching your head, we need more details. Does the car have an aftermarket immobilizer? Sometimes these are very particular things and something like a battery change [in either car or remote] can cause funky issues... At this point if you're not running tow it to the dealer, because that's the extent of my knowledge.
Good luck.