1996 4runner won't start

Please help. The other day when I opened my car door the alarm went off. Although I do not think the alarm was armed. My car would not turn over. I put new batteries in my key alarm control. I could not get the alarm to quit going off. Finally, it did but the car would not start. I switched the alarm valet to disable the alarm. Still the car would not start, would not even turn over, it seemed like there was no power whatsoever. We took the battery to buy a new one. However, NTB told us the battery was fine and fully charged. We put the battery back in the car and jumped it and it worked. Then it worked fine. The alarm is still disabled and now the car won't start again. There is no power at all - you can't even lock all the doors with the key from the drivers side door. Does anyone know what is going on or what I should check? My husband is out of town with the car and stranded.
TIA,

Bad connections at or around the battery connections make sure they are clean & tight.