This is from NFS Wiki page, it will not run well under Vista, so will probably have issues with Win 7. Check the support page for the game for updated patches that may help.
"The unpatched Windows version of the game has compatibility issues when playing under Windows Vista and crashes after the EA Logo screen, although most issues have been resolved in patch version 1.4. According to EA's Website Support page, they have not released any games that are supported under Windows Vista and suggest changing the compatibility mode to Windows 98 to play EA games if necessary.
In versions prior to 1.4, the game will load with both 32-bit and 64-bit editions of Windows Vista if the compatibility mode is changed to either Windows 98 or 95. However, the game still crashes frequently. Deleting or renaming the MOVIES folder, however, alleviates the problem. This has also been linked to the 1.3 upgrade patch. Some users have also successfully run the game out of the box on Vista 32-Bit RTM, which suggests that the issue may have been related to issues in Vista's pre-release code."