I struggled to get Minecraft up and running on my laptop (Ubuntu 10.04). I copied an older user folder from a windows machine, and nothing worked – I only got a black screen after starting the game. This seems to be quite common, and seems to be cause by library mismatches.
There are a million complicated howtos out there how to fix this, but for me it was sufficient to let Minecraft re-download all its libraries:
Then, start the game and wait for the download to finish. Et voila!
The folder on windows is %APPDATA%\Roaming\.minecraft\bin\. An alternative route is to select “force update” in the Minecraft option screen.