When you hear a clicking noise is most likely a battery problem however you stated that the battery was replaced so i suggest you check the condition of your cables look for rust or corrosion etc.
check your battery then the connections if it still wont start try changing the starter solenoid if possible
If it isn't starting you have another problem.
if you recently replaced, charged, or "boosted" your battery, similiar problems like this, i have yet to find an answer on how to fix it other then takeing it to a dealer and have them restore your vehicles configuration.
Sounds like the ignition switch.
Yes.
under the hood
Same thing happened to my 1998 Dodge Durango and I had to replace the battery connector wires...like $30...
I recently had the fuel pump replaced in my Dodge Ram 1500 ... same process. $500.00
I just went through this with my 1998 Durango, it ended up being the ignition coil. Costs about $37.99 and takes about 20 minutes to change, a very easy fix.
Under the front passenger seat
Its under the front passenger seat
I do not know, I have a 1999 and mine quit just about two months ago, I have replaced the battery and that didn't help, maybe you should try your battery though. I will probably just order a new keyless entry.