My Inspiron 5000e notebook is turning itself off constantly. I will be doing any of a variety of activities on my notebook, and it will suddenly power off without any warning or prompting. This occurs when the notebook is being powered by the battery and when the notebook is being powered through an electrical socket.

This is the second time I have encountered such a problem. The first time was about six months ago. At the time, the battery on the notebook was not working well - a full charge would last for only about fifteen minutes. When I purchased a replacement battery, the problem went away completely. Unfortunately the replacement battery is now lasting only about fifteen minutes when fully charged, and the "powering off" problem has resurfaced as well.

How can I correct this situation? I do not care about running my computer through a battery - I am always near an electrical socket when using it anyway. I just want the computer to stop turning itself off. Please advise.