I believe the problem may be the cooling fan, of the Fan Assembly.
Dirt, dust, hair, food crumbs, lint, you name it, can be drawn up into the laptop by this fan.
This can cause a strain on the fan's bearings.
It could also be that the fan's bearings have simply failed. They are dry, hence the occasional howling noise.
The method is to open the laptop, and physically check the fan.
Dell Support > Inspiron 5100 Notebook PC > Service Manual,http://support.dell.com/support/edocs/systems/ins5100/en/sm/index.htm
FOLLOW Anti-Static Precautions.
Your body carries Static electricity. Static WILL fry out (Short Circuit), the delicate hardware components inside a computer.
Suggest wear an ESD wrist strap, and connect it's alligator clip to a good ground source. (Electro Static Discharge)
Basic example of an ESD wrist strap,http://www.radioshack.com/product/index.jsp?productId=2103245
[ I connect to an unpainted surface, of the metal frame of an open, empty desktop computer case. Just one example ]
On the Dell Support > Service Manual page, click on -
Microprocessor Thermal-Cooling Assembly
This shows the Fan Assembly. It is connected to the Microprocessor Thermal-Cooling Assembly.
Another view of the Fan Assembly,http://www.brilliantstore.com/laptop-cooling-pad-dell-cpa-1606.html
View of the Microprocessor Thermal-Cooling Assembly, with the Fan Assembly,http://www.laptopbattery-usa.com/dell-inspiron-1100-5100-5150-laptop-cpu-cooling-fan-p-1238.html?zenid=okh2t54jgsg369stoj7gipf3k5
See the 4 screws sticking up, and the squarish metal plate they go down in?
This plate sits on top of the Processor.
The two curved slightly flattened copper pipes, are Cooling Tubes.
They are sealed on both ends, and are filled with Nitrogen.
They attach to the squarish metal plate, that sits on top of the Processor, and the other end of them goes to a Heatsink.
This cannot be seen in the photo.
The Heatsink is a rectangular finned object.
Has Tall, Thin, fins.
Heat is absorbed from the Processor, by the squarish metal plate sitting on top of it.The Cooling Tubes then absorb the heat from the squarish metal plate.
Heat is then transferred along the Cooling Tubes, to the Heatsink.
The Heatsink absorbs the heat, then radiates it away with it's fins.
Air from the Fan Assembly, helps carry heat away from the Heatsink fins.
The Fan's blades, center hub, and surrounding cage, (Shroud), must be clean. If the fan's blades are dirty, the result could be an unbalanced fan.
Makes the fan tilt to one side, and possibly scrape the blades on the Shroud.
Also over time the dirt, dust, etc, can cause the Fan's bearings to fail.
Gently see if you can move the Fan up, and down. Gently grab a blade of the Fan, and see if you can move the Fan. You will know if the Fan's blades have too much movement up, and down. (Or tilt to the side)
If the Fan is bad, (Bearings), see if you can buy just the Fan, and replace it.
If not you may wish to replace the entire Microprocessor Thermal-Cooling Assembly.
Should this be the case post back in a Comment.
I need to guide you in proper replacement.
[ You need to Thoroughly clean the top of the Processor, and the bottom of the squarish metal plate that sits on it.
Then Thermal Paste needs to be Properly applied, and the 4 screws tightened down in a sequence ]