Trouble starting 92 accord

Looking for some help. I have a 92 accord LX which lately is giving me
trouble starting. When I turn the key on It cranks (I see the the
pulley moving very slowly) but it won't start, then eventually it runs
out of juice and I can't crank it anymore. If I jump it then I can
start it. I thought my battery was dying on me so I replaced it with a
new one. Anybody has any ideas?

 

Maybe your starter is putting out too much negativity. (Starter going
bad perhaps?)

 

You should have checked the state of charge of the battery before replacing
it. Multimeters are cheap.

Turn on your dome light. Now try to crank. Does the light dim to nothing?
Does it dim just a little? No dimming at all?

You either have a bad starter, or dirty connections to the starter and/or
battery. At this point I'd say dirty connections at the battery/starter.
Also check the engine ground cable as well. If it breaks, it can interfere
with starting.

See here for more:
http://www.tegger.com/hondafaq/startproblems.html