Hi donnar89688245,
If you have purchased Acrobat 8 standard from Adobe you will be able to see the download link in our Adobe account.
Unless your new PC is running Windows XP or Vista Acrobat 8 is will not be fully functional Like Windows XP. Acrobat 8 is no longer supported by Adobe Product Life Cycles & the direct download link doesn't exist anymore.
Because you version is so old, there is no upgrade discount available. You might have to purchase Acrobat DC Plans and pricing | Adobe Acrobat DC
Regards,
Aadesh