Have to push start truck

I changed starter and it started a couple of
times then let it set for an hour went out
same thang  I all so have ignition lock on the
truck we also change the relay switch but
then put the old one back in then took the
starter in the starter read good put the old
starter back in took the old starter back out
put a new starter in and it fired right up
drove it to two different destination and then
came home now the same thing when I
blow in my ignition lock like a clicking noise
at the relay and that's all I'm getting the
voltage is a little bit down not too bad
though but once I get it running once I push
start it it runs great can you tell me what
might be wrong