As your product came with the new computer, the problem can only be solved by the OEM (Original Equipment Maker) because they know or should know what the serial number is for their product.
If you want to get PSE11 then you can buy it from Amazon and it will workout cheaper than buying an upgrade from Adobe IMHO.
If you want both PSE11 and PE11 then this is the link:
Please also make sure you want to buy a boxed version so9 that it comes with the media that can act as your backup for future re-installation.
Finally, please note that you don't need to post your email on a public forum like this one because we, volunteers, don't reply directly to Adobe customers. You will get copies of replies in your email account that you used to post this question.