The only person that can help you with this is one man.  techknight.

couple things though.

The Charging circuit is designed for 1500ma max.

and the on board battery needs to be installed.

do not run the portable with out a lead acid battery installed,

as i believe it does more then just provide the system power as some filtering.

usually when a portable does that, ( works when charger is attached ) but will not stay on after unplugged.

if you monitor the +5 rail you will notice that it does not remain stable as soon as the Charger is disconnected

and that is because there are rotted traces and the Voltage ref is probably no longer connected to the 5 volt regulator.

or the 5v regulator is bad or is rotted up... 

Flat out what you are dealing with here is CAP GOO ROT..

these scenarios are a product of Via rot, Trace rot, Pad rot.

so its going to be up to you to meter out the lines and figure out the problem.

i'v wanted to put together a document that includes specifics,  ( when 5120/5126 does this.. )  

(try this) kind of thing, but i have no time for that any more. 

there are pattern failures with these things,  but right now only techkinght has all this valuable information in his head

that is why, I and pretty much everyone else in the world have been simply sending these boards to Mike, 

because he is just the portable master.   he's probably been through at least couple hundred boards by now

and has all kinds of proprietary hand drawn schematics and diagrams .  and he is worth the $50 an hour he asks for.