It is possible that the Audio Jack that you are plugging the external speakers into is faulty here.
These have a switch in them that stops a signal to the Internal Speakers when external; speakers are plugged in. If this switch is stuck in the Off Position it will cause this problem to occur.
If that is the case unfortunately it requires the Audio Jack to be replaced and as this is part of the M'Board many repairers want to fit a new M'Board. As they do not have the equipment or resources to replace the faulty Jack.
Any way this [b]Is Not[/b] a software issue but a hardware issue. There are many possibilities ranging from the internal speakers being disconnected to broken Signal Leads to the Speakers or as already mentioned a Faulty Jack for the external Speakers.
No matter what though it requires that the unit be pulled apart to Fault Find the problem and repair as necessary. If you are not comfortable with dismantling this unit it should be done by an Authorized Repair Agent who has direct access to the Official Spare Parts for this NB.
You can find the Dell Service Manual for this unit located here
http://supportapj.dell.com/support/edocs/systems/latd830/en/SM_EN/begin.htm
But you should first read the warnings before you start to dismantle the unit.
Col