Laptop running only on AC power

My Compaq Presario CQ57 started giving me problems a few months ago - the battery charged fine, but even with a fully charged battery, if I took it off of the AC adapter, it would crash within minutes. So, major nuisance, but I could deal with it.

Within the past day, it won't run for more than maybe two minutes. Not even long enough to run any kind of diagnostic, so I don't know why it's suddenly decided not to function. I can get it to at least begin booting with the battery, it seems to be hit-or-miss on whether it wants to even begin to boot on AC.

Any thoughts? [Other than needing a new laptop?]

is the power light on when the power adapter connected to the laptop? does the power adapter have a light on it as some power adapters do?

And this is why troubleshooting the computer at 4 am is a bad idea.... the reason it was behaving differently was due to a difference in circumstances - namely the power cord coming loose from the brick, so it was effectively unplugged.

So now it appears to be back to the same state that it's been in for the past couple months. But so long as I'm already asking, and given that that state is definitely not "working properly", what might cause that problem? The battery charges fine, but the computer won't run off of it for more than a few seconds to a few minutes at the outside. Then it acts like there is no battery [that is, it's not like it behaves like a low battery situation, it behaves like a no-power situation] and crashes.

how old is the laptop & battery?