That is most likely what is wrong and this happens because people do not disconnect the Power Adapter before attempting to place the NB into it's bag or move it around with the Mains Adapter still present.
This causes the Solder Joints to break and the Power Jack to lift off the M'Board or otherwise break and not supply power tot he NB.
As for replacing the Jack it may not be necessary if you have the right qualifications and tools. It is quite often possible to solder these back onto the M'Board if the M'Board has not been broken and you use caution. You do need a Electronics Soldering Iron that is Temp Controlled to something like 312 C and High Silver Solder suitable for Electronic Work not Jewelry repairs.
You need to completely dismantle the NB and remove the M'Board from the Chassis so you would need the Dell Service Manual which is available from Dell's Web Site here
http://supportapj.dell.com/support/edocs/systems/latd600/sm/index.htm
But unless you have the correct Equipment I would advise you to take it to a Computer repair Shop as the chances of destroying the M'Board are very high through poor Static Control Procedures and damage from the incorrect tools required to repair this with.
Col