DELL fans can be loud.
They may be old and stop working.

The Dell fans use a proprietary plug to attach to the motherboard so youI will either need to run the fan directly from the PSU or you may try cutting the dell connecter off and connecting it to the new fan to avoid getting a fan error message each time on boot or you can turn off the error message.

If you call DELL, after waiting for a LONG time, you will either be given sorry it is not in stock or a very high price.

You can find some fans to do the job DELL REPLACEMENT FANS ON EBAY .

These fans can be used for:

Dell Dimension 2300, 2400, 3000, 4600 8100
Precision Fan 330/410/420/610/8100
OPTIPLEX 170L.
And even may be some more:

To be sure, just check the dimensions of the fan:

Distance between screw holes: 82.50mm

Thickness: 25.4mm = 1 inch

The 3 pin connector will probably not fit. You should use the 4pin molex connector, the ones that are used by the CD-ROM, hard drive, and DVD optic drives.

When using the 4pin connector, the fan will work just fine.  However, your computer may think there is no fan installed because of not using the motherboard connector.  You simply can turn off the fan detector to avoid warnings.
The settings are located in Power Management section of BIOS.
Use following settings

Low Power Mode OFF
Suspend Mode S1

If you don't see any options like Power Management (although you looked for it long enough), you may have a VERY OLD BIOS. You can easily update your BIOS. If you have no clue or courage to update your BIOS, you are strongly advised not to worry about it too much. Call DELL ..

Here is an other alternative from a fellow Dimension User, courtesy of Adam Vandenberg:

"We have a Dell Dimension 8100 (desktop machine), which is notorious for its CPU fan. For whatever reason, Dell used a proprietary 3-pin motherboard connector for the fan. When the fan starts going out, it gets really loud, but the part is out of stock. Disconnecting the stock fan from the motherboard means that on every boot, you get a beep and have to hit "F1" to bypass the missing fan.

....

To use this fan to replace the Dell Dimension 8100 fan:
* Disconnect the existing CPU fan from the motherboard, noting which pin is connected to the white wire. This is the fan sense pin.
* Using pliers, carefully remove the plastic sheath on the motherboard fan pins.
* Using the 4pin connector, connect the fan to a power supply socket.
* Using other branch of the cable, with the white wire to a 3-pin plug, connect ONLY the wired pin to the fan sense pin on the motherboard.

The Dell will then detect the new fan and bypass the warning message.
As a bonus, this fan moves more air on its high setting than the stock fan did.