i would think if it was the adapter the laptop wouldn't turn on at all ? sounds like a battery issue either the battery itself or tha associated wiring inside the laptop. some trial and error investigative procedures are probably needed

i have used these in college and worked many dell d620 laptop and i can tell you from past experence its the battery.. i hope you have already replaced it with a new one..

i purchased an aftermarket type and it lasted serveral hours; for the money it was a good buy...

don't leave your laptop connected to the charger for extended periods of time....

the dell d620 are old but still durable workhorses; espiecially for the telemarketers.. its slim, got lots of power nice wide screen and can take a beating..... parts are easy to find and very affordable.. Dell licked the spoon with this model and called it good... the rest is history...

enjoy.....