I recently replaced the fan on my in-laws' 2350 because it too was running near full speed all the time.
I even pulled the CPU, applied some good thermal paste and dusted to get optimal cooling but the fan still would run at high rpm. I ended up replacing the fan to get rid of the problem.
The stock fan has a built-in thermistor that speeds up the fan when the case gets hot but I think after these 8 years it wore out and does not adjust the speed properly.
I suggest you replace the fan. Any 3-pin 92mm fan will do... I went with a fan that runs at a constant rpm that is quiet. If you want a replacement fan that also has a thermistor to control fan speed, Gelid makes a very good one (I have the 80mm and 120mm variant). Moves good air and is quiet. Place the temp sensor anywhere inside the Dell case and it will speed up or slow down as needed.
Here is the link:http://www.newegg.com/Product/Product.aspx?Item=N82E16835426004