I have a ThinkPad T42 model number 2379 DXU. I just bought an internal
DVD Burner-ThinkPad Multi-Burner Plus Ultrabay Slim Drive 
Which softwear should I buy?  Also what do you
think of easydownload.com who have IcopyDVDs2?

I would suggest NERO software for disc burning needs and PowerDVD for
playing DVD movies. I use both of these and they are fantastic program
and are HIGHLY reliable and world renowned.

Are you planning on burning DVD movies or simply data DVDs? If you're
burning movies, a program like DVD Shrink (http://www.dvdshrink.org/)
would be good for fitting the entire feature on a DVD-R with quality
loss at a minimum.

I would also recommend NERO 6 and Power DVD for both burning and
watching movies. NERO 6 can be oobtained for an extremely low price
(OEM) from monarchcomputer.com, if you're purchasing additional
hardware (like maybe replacing the drive in your desktop with a new
DVD burner..?) PowerDVD 5 can also be obtained cheaply from the same
website via OEM purchasing. It may be possible to get PowerDVD 6 at a
discount if you have a PowerDVD 5 disc, but I'm not sure if cyberlink
(the company that makes PowerDVD) provides an upgrade program
structured like that.