The computer will not recognize the AC adapter

My brother left a plug-in for his computer at a friends house, you need it so he can use the adapter he has with his computer. He asked me for mine, and it is different, its a Kensignton and has never failed on me, unlike the ones I purchased from Dell, until now. Then he lent me his, which would go into my computer without his missing plug-in. Mine rechanged his, but his would not, only keep it on. I thought it was ok, as long as he juiced his computer up I would take mine back.

This morning I pluged mine back into my laptop, a Dell Ispiron E1705, and it is not rechanging my computer at all. I tried turning off my computer but the low battery mode put it on hibernate before I could do it. I turn my computer back on and it gives me a message somewhat along the lines of: "The computer does not recognize the AC adapter, it will not rechange your battery. Please use (some model number) Dell adapter." And then it gives me a list of comands to run diagnosis and so forth. without knowing what to do I just chose F1 which is normal reboot.

I really need help fixing this issue. Please, if anyone can help me I would appreciate it.