Hey,
My 76 did the same thing as youre describing, and its a lack of power to the starter. The solenoid is engaging, but the starter doesnt have enough power to churn the engine. Heres what could be the problem w/ your battery.
1. Not enough CA (cranking amps), get a more powerful one.
2. Dirty or loose battery connections, wire brush/ clean the connections and make them tiiiight.
3. If your batter is like my old one, it will hold charge, but the second you try to start it, it dies. Check this by having a door open and the overhead light will be on, it should be bright. Then try to start the engine with the door open and if it goes black and clicks, you need a new battery.
4. Silly things, dont get my wrong, this fooled me too

. If its an automatic, it wont start ing gear and sometimes i have to hold the brake pedal on mine, but most likely thats not the case.
Enjoy