Had this same problem today.
EA tech emailed this reply:

After backing up registry,

"Go to Start -> Run -> type in "regedit". There is a registry key that causes this and must be removed. It is found in:

HKEY_LOCAL_MACHINESoftwareMicrosoftWindowsCurrentV ersionUninstall{0DEA94ED-915A-4834-A87E-388D012C8E02}

This whole key should be deleted and after uninstalling once more, the game
should install normally."

Worked for me