1966 Chevrolet Impala won't start without a jump

Hi, My 66 Chevy Impala will not start without being jumpstarted. I replaced the starter/solenoid a couple weeks ago and the car worked fine. Just recently I try to start the car and nothing happens other than the dash lights come on. The battery is about a mth old and the alternater still looks fairly new. When I get a jump from someone the car starts up fine with no problem. I would appreciate your help with this problem. Thank you.