According to Dell's specifications, that laptop would need a 45-watt or 65-watt AC adapter. Since your 135-watt adapter was recognized by that laptop's BIOS and charged the battery, I'd say that the user's adapter is the problem. He needs a genuine Dell 45-watt or 65-watt (may depend upon the laptop's components) adapter. You could check to see if his current Dell adapter has a bent or broken pin in the barrel connector. He may need a new Dell adapter. And, I would do this: Disconnect the AC adapter.Disconnect the battery.Press and hold the power button for 30 seconds to discharge any residual electricity.Reconnect the AC adapterReboot the laptop. As for battery, you can test it.  Open an Administrator CMD prompt (CMD, run as Administrator).Paste this command, and then press Enter:powercfg /batteryreport That will show a figure for the designed battery capacity (when new) and the current capacity. If you buy a new battery, ensure that it is a genuine Dell battery.  
I have an odd problem with a Vostro 3500 laptop. Warranty ran out 10 months ago. Plugging in a generic 65W or genuine Dell 45W adapter yields the message from the Dell Power manager that "The power adapter attached to your system is not recognized. Attach a supported power adapter with at least 45 watts." I'm the IT provider for the customer who owns the laptop and they have so many laptops floating around that I can't guarantee the genuine Dell power adapter is the one that came with it. It does have the center pin on the plug. When I first got the laptop to diagnose, the battery power was completely gone. In fact, running the Dell startup diagnostics said the battery was missing (it's really there and plugged in). Plugging in the 2 aforementioned power adapters would allow the laptop to run, but the light next to the power jack would blink 4 or 5 times amber and then 1 time white over and over. BIOS says that the AC adapter is not installed. I happen to have a genuine Dell 135W power adapter and I plugged it in and the laptop started, the light next to the jack was solid white and the BIOS said it was a 135W power supply. The battery charged to 100% and the laptop ran on battery after unplugging it. I understand that there is a special chip in the new genuine power adapters that communicates with the BIOS in the new laptops to indicate that the power adapter is of the proper wattage and is a genuine Dell. Dell support says the power adapter with the laptop was part KXTTW. A google search shows that's model number LA45NM140 which is the exact part number on the genuine Dell 45W adapter that no longer charges (but does power up) the laptop. Has anyone else experience this type issue and what do you think the next step is in diagnosing this? I did order a new battery, so I'll see if that's the issue. Thanks for your assistance.
Vostro 3500 Power Adapter is not Recognized