I've got an Inspiron 17 5000, 4 months old. Was working fine.
Now, all of a sudden, it won't work unless plugged it. Says 'plugged in, not charging'. Won't switch on unless plugged in, if unplugged whilst on immediately shuts down.
I've run SupportAssist, which says the battery is fine. I've removed the battery, wiped it clean, and replaced it. Don't know what else to try.
If there are no other symptoms (check setup - F2 at power-up to verify the AC adapter is recognized), call Dell and have the battery replaced under warranty.