All the drivers for the T3400 are available here. Be sure to select the correct OS at the top before downloading any drivers. Use the "Single File" download option because the Download Manager can cause problems.
You'll need to know which video hardware, audio hardware, etc are installed so you can get the right drivers and they have to be installed in the correct order. In theory, the Service Tag should filter the list of drivers to help you find those specific for this system's original configuration, but -unfortunately- that hasn't worked correctly in a long time. 
Drivers can be downloaded on any PC and burned onto a CD/DVD for transfer to the T3400.
Once all the drivers are installed, be sure to go to the Microsoft Update site to download the Service Pack and all subsequent updates and hotfixes.
Note that Dell doesn't provide a "Recovery disk". The disk they provide installs Windows and nothing else. The user has to install all the drivers etc after Windows is loaded. In a typical system, there's a "Recovery Partition" on the hard drive that resets everything to the factory state with the OS, drivers and Dell's preloaded software. But none of that will be available if the drive has been wiped or replaced.
OOPS! Osprey types faster than I do.