NIS on new computer after old computer died?

Hello.  My old computer died - mother board kaput. I had NIS 2011 on it with about 9 months left.  I bought a new laptop and it has a trial version of NIS that expires in 6 days.  I'm tyring to get the NIS that was on my old computer on the new computer so that I don't lose those 9 months that I've already purchased.  I tried downloading it and the download appeared to work correctly but it doesn't show up anywhere.  The trial version continues to run.  The old computer was Vista; the new one is Seven.

Do I need to uninstall the trial version before downloading NIS 2011?  If so, what's the best way to do that?  I noticed there is a Norton product remover.  Do I use that or just the uninstall software from my computer?

I have the product key from the original version.

Thanks.