wife's car wont start

ok my wife's 95 civic isnt starting. when you turn the key none of the lights come on. also it wont start from popping the clutch. it will how ever start from a jump start if left to charge for a couple of minutes. i tested the battery (which is a new battery) still has 13 reading. So i thought perhaps the alternator wasnt charging the battery. so once car was running i unplugged the positive cable on the battery, and the car continued to run... the car doesnt seem to cut "on" with power unless its on the jumpers, even if the battery has a charge. it has new battery terminals also, i checked all those and looked ok. any ideas of what i could try next?

ok so i was messing with it some more while the rain slowed down a bit. what its doing:

when you put in the key, and turn it one click, all seems fine, go to the 2nd click and the car like looses power and also will not turn over if cranks, no lights in the dash nuttin, like the keys arent even in the ignition. checked the battery charge again, reads 13. then i hooked up jumper cables, and when you go to the 2nd click on the ignition this time, the dash lights all come on and when cranked it starts. then i took off the jumper cables, leaving the car running, tested the battery again and read 13.6-.13.8 meaning the alternator is charging the battery. turn the car off and try to start again with out cables nutting back to no power on the 2nd ignition click...

is this my ignition switch going bad? not sure how the jumper cables play a factor in that...
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If the battery terminals are clean and tight, what about corrosion working up into the positive side cable?
The insultaion from the positive wire could mask the problem!

This could cause resistance, and the wouldn't get the charge from the Alternator thats needed to start engine.

could it be your starter as the posative cable runs to it? the starter may have a short?

well its new terminals, when i replaced the battery, i also replaced the terminals because she was getting corrosion on the terminals. whats confusing me is on hondas there are 2 wires coming from the battery pos terminal, one runs straight to the starter, and the other to the fuse box then to the rest of the car. when the ignition is in the "on" position and the car has no power as if the key wasnt in the car and the car was off. how would the starter mess with the wire that runs to the rest of the car? and how does adding jumpercable bypass that, because its still running thru the same cables?

or is it that having 2 batteries hooked up causes double amperage, enough to get thru the cables? i guess that could make sense, cause when it is running and off the cables it doesnt sounds as strong as it normal does. hmm maybe i'll try replacing the entire cables.

ok when your jumping the car your pushing more amps. to your starter.

ok right on point man! i inspected the cables and they looks sparkling clean, but where the plastic was i couldnt tell, so i kinda moved the cable around trying work off and inside corrosion to see if it made a difference and she started right up, actually better then she has in a long time! so she is good for now, gonna pick up some new cables tomorrow! good job!

yah the post on battery could've been glazed as you say you clean them or just moved it around. if battery is not sealed i'd check the water in it since you found corrosion.

that would be a good idea on replacing hole cable or cables?

Sounds like a bad ignition switch to me, electrical portion.