My Dell Inspiron 1501 keeps turning off unexpectedly. It doesn't want to turn back on again, but when it finally does it only says "your computer shut down unexpectedly" but when I restart it normally again it offers know explaination or indication that there was ever a problem.

SOURCE: Dell Inspiron 8600 - overheating and shutting down

Start by cleaning the fan and heat sink. Dirt or dust build up can cause them not to work as efficiently as they should. If cleaning doesn't fix it, you might consider replacing the fan and heat sink or purchasing a cooling pad.

SOURCE: dell inspiron 1501 work fine turn off last night now wont turn on

You mentioned trying a different battery, try a different AC adapter.

When plugging in the ac adapter to the wall, see if the POWER LED comes on on the adapter, then when you connect it to the computer, see if the LED stays on.

If the issue occurs with both AC adapters (No battery installed) then the motherboard has failed. If one ac adapter works but the other doesn't then the adapter is bad

SOURCE: Dell Inspiron 530 randomly shuts down and restarts

Sounds like it could be a virus. Or, a heat buildup problem - are all fans inside machine working? Is the fan inside the power supply operating? Was there any work done inside the computer recently?
If the hdw is all ok, go out and buy yourself a copy of Norton Internet Security 2009 - 1 user lic - $49.99 @ Staples. Do *not* buy any earlier vers. of this software! Install, update it, run computer computer scan - probably will find/remove some/many viruses.

If this helps, please take the time to rate my response to you.
Thanks and good luck.

gurutim

SOURCE: dell inspiron 1501 shuts down very often

is the laptop running unusually quiet? when you start it up hold it up to your ear and see if you can hear a fan spinning. its not uncommon for a laptops cooling fan to come from factory jammed. if its stuck you can usually dislodge it with a firm smack (after the laptop has been cut off and battery removed, wait a few seconds to make sure the hard drive has spun down).

SOURCE: Dell Inspiron 1501 Touchpad locked up

Check the system setup F2 at start, and ensure the touchpad is enabled, next try an external mouse, see if it works.
If and external mouse works, the touch pad has failed and a new palmrest is needed.