Lisa's parents just got a new computer when their laptop stopped working, so I snagged it for the boys and I'm hoping to resurrect it.  Here's what it does - when I plug it in with the battery out of it, the green light power light (showing it's plugged in) comes on, but if I hit the "on" button the light goes out and nothing happens.  I have to then wait for about 10 seconds before plugging it in again to get the light to come on.

If I plug it in with the battery in it, nothing happens at all, BUT, if I slide the battery in when the green light is on, the "charging battery" light comes on.  Again, though, if I try to turn it on, both lights go out and nothing happens.

Apparently as the computer was dying there was a period of time when it would run sporadically without the battery in it, but never when the battery was installed.

Does this sound like anything?  Could a power supply cause those sorts of symptoms?

Sounds like my old laptop, if you jacked with it long enough it would take a charge but it was a PITA. Might need a new battery too

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My wife's old laptop is similar although not nearly that bad. Basically if you let the battery run dead, then when it's plugged in and running it always showed the battery at 0% capacity. Finially just just it down, plugged it in, and let it sit for a couple weeks, and low and behold the battery light was green and it said it was charged. Then it would actually run on battery only for a few minutes, but if you let it go dead the whole process started over.

To me it sounds like either the internal power supply has a problem, or your power brick is dying/dead. Is there any way you can cut/splice into the wires on the power brick and check to see what it's voltage is when disconnected, connected, and trying to power on? I'm guessing it's full voltage when disconnected, drops a little when you plug it into the laptop, and drops to almost nothing when you hit the power button.

If the power brick is fine, then a new battery would definitely be worth a try, but I think the battery was probably just acting as a 'buffer' to supplement the power brick during high load, and now that the battery is dead, the brick can't pull the load on it's own.

Unless its a brand name (like Dell) and it's not real old, good luck finding parts. New battery would NOT expect to fix it and it'll run you some bucks, depending ($50+ likely, 100+ for some models). So you buy a very expensive battery and it's still broke and now you have a battery that's good for nothing. If it was anything cheap to begin with, it's probably land fill material. Good luck.

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I came across some "ask a tech" type website last night and they thought it was likely the power controls on the main board, although I still think what Ian is describing makes a lot of sense, that there's just barely enough power getting through the brick to light that light, and then when it gets the load of trying to turn on it just craps out. 

It's a Compaq Presario 1500 which wasn't a bad deal in it's day - 2GHz Pentium IV, 20G hard drive, 128MB RAM, so I'd like to get it going so the boys have something for homework.  It looks like motherboards for it are about $100, though, and I don't want to do that only to find out it was just the power adaptor, you know? Starting to feel like a car.