Could be a starter fault draining the battery without pushing the power out at engine end. I had this trouble many yrs ago same symptoms.
Check all the leads from battery to starter also engine earth.
however take note of other comments if the battery is 3 or more yrs old.
Bob
February 2014
A drop test on the Battery might be a good idea
John
February 2014
Has the battery been tested,sounds as if it is on the way out,any doubt, replace
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