sometimes during downloads and at just random times. If it gets to working too hard it will shut itself off and I get an image that shows a monitor, the box and a cord connecting the 2 with an x through the cord. All I have to do is turn off in the back and turn back on and it starts right up again. It doesn't do it for every download, just some of the more difficult ones. Any ideas on what to do?

Welcome to Techspot!
It would better for you to fill out your Profile and give us some details when you post a problem.
What operating system you have?
Have you gotten any error messages,etc.
That little computer with the line through sounds like your losing connection to the web.
Are you on dial up?
You may have a hardware problem ,eg. power supply?

computer shuts down win xp

G;
Laptops do not lend themselves easily to hardware troubleshooting. There are some software issues that can cause the problems you are having, and since you know what is on your machine ,I suggest you do some investigation at Microsoft kb .Updates for XP can actually address some of these.Also check you are up to date with drivers ,firmware , etc at NEC.
Are you not getting any Error messages,event log system errors?
Did you make any changes when this started? try to load a restore point from before your problem started.