My laptop (Dell Inspiron 600 m / Windows XP) gets very hot (except the battery portion). Till a few months back, the fan would start running within an hour of switching on. However, I haven't heard the fan sound (or noise) for months. Is there a way (software trigger etc ) to find out if it's working without getting the laptop manually inspected ?

Also, I have been facing 100% CPU usage problem. Are these two related ?

Thanks in advance for any suggestions.

You might want to invest in a laptop fan stand. You can find them for $10-$20 at Radioshack or search Newegg.com for it.

Its recommended to use these laptop fans cause the laptops weren't built to be used for a long period of time.

Your Dell should briefly initialise the fan as soon as you turn it on (during the POST boot). So you should be able to feel the brief gust of air coming from the fan duct. I believe the temperature sensor for the fan is located beneath the processor, which is best repaired buy an authorised dealer.
However if your processor is reporting a 100% usage, then your fan SHOULD be running flat out, just to dissipate the heat generated from the processor.
Get it checked out before your processor gets cooked