no power to van

Our Odyssey has recently had issues starting where it seemed to not start quickly.  The other day I had to change a headlamp and while changing it, I noticed there was a lot of buildup on the battery terminals.  A few days later (weekend) I decided to clean the battery connections thinking that will help them make better contact to start the van quicker.  After taking them off and cleaning them, the van was experiencing issues with having any power at all.  When trying to start, there was no power at all.  So I tried to jumpstart the engine...still no power at all!  I removed the terminal connectors and reattached them, moving the + connector around a little.  There was a 'clicking' noise coming from the engine compartment.  I then tried to restart the van...had dash lights but not enough power to start...tried to jumpstart and viola...it started.  Ran it for a while, then turned it off....would not restart.  Thinking it's probably a battery issue because we live in AZ and it's a fairly old battery anyway (and the + terminal seemed to move more than it should), I went and bought a brand new battery.  Hooked it up and absolutely no power at all....try to jumpstart, no power at all....anyone have any ideas??