If the PC crashed when new and reinstalling the OS didn't resolve it, HP support should have had you send in the PC for repair or take it back to the retailer as it sounds like a hardware problem.
If you purchased OneCare and activated a subscription, but now have no need for it since you have a Mac, you may be able to obtain a refund.
If it is a retail copy, and you are in North America,
http://www.microsoft.com/mscorp/productrefund/refund.asp
If you purchased online (though I can't imagine how if the PC crashed upon booting...) contact support to cancel the subscription and obtain a refund -
How to reach support (FAQ) - http://forums.microsoft.com/WindowsOneCare/ShowPost.aspx?PostID=2421771&SiteID=2
On the other hand, if you have an active subscription, which is what was created when you activated on the first computer, you need to use the same LiveID on the subsequent activations. You can't use the same key twice. If you are arriving at a screen to purchase or provide a token, you are likely not using the same LiveID as the subscription ID.
If you don't recall the LiveID you used for your subscription, you will need to contact support who can provide that information to you using your Key and/or contact information.
How to reach support (FAQ) - http://forums.microsoft.com/WindowsOneCare/ShowPost.aspx?PostID=2421771&SiteID=2
Alternatively, sign in at http://billing.microsoft.com with email addresses that you have set up as LiveIDs and one will show your subscription listed - that would the LiveID to use to activate with.
If the activation dialog already contains a LiveID from a prior attempt or one used in trial mode, but this is not the one you need to activate with to associate it with your subscription, see this post for how to reset this - http://forums.microsoft.com/WindowsOneCare/ShowPost.aspx?PostID=2776450&SiteID=2
-steve
