1997 Chevy Lumina Battery Drain?

My 1997 3.1L V6 chevy lumina wont start anymore when I try to start it. I thought it was the battery because the cars getting power to radio and lights and everything else but it wont get enough power to start, only rapid clicking when the key was turned. I had to end up jumping it almost every day with another car or portable jumb box just to get it to start due to what seemed a completely drained battery. I decided to replace the battery. But now the car won't turn over and I don't even hear the rapid clicking anymore. Ever since the original battery was disconnected, the car won't start at all anymore, even with jumper cables connected to a running vehicle. I have tried two different batteries with the same results. Someone told me it could be my solenoid, can anyone please help?

I replaced the original battery with two different batteries. Checked and cleaned all leads, terminals and connectors for battery. Don't have access to a voltage meter, but am confident that every replacement battery tried has a good strong charge.