You likely cannot uninstall anything from a dead computer, but you don't need to uninstall Lightroom anyways. You can contact Adobe support by chat to have them deactivate the program for the dead machine.
Serial number and activation chat support (non-CC)
http://helpx.adobe.com/x-productkb/global/service1.html ( http://adobe.ly/1aYjbSC )
As far as getting the application on a new machine you will need to download it and use your serial number to activate it. The following link should help for downloading...
Lightroom - all versions
Windows
http://www.adobe.com/support/downloads/product.jsp?product=113&platform=Windows
Mac
http://www.adobe.com/support/downloads/product.jsp?product=113&platform=Macintosh
In the event you run into any issues with deactivating the original installation, your license allows you to have the software installed/activated on two machines, so you can still proceed with getting it installed on the new machine.