I think it's not an issue with slackware64. It's probably between ati and the 2.6.29.x kernels... check this topics:
ATI driver with kernel 18.104.22.168
ATI fglrx 9.5 on Slackware 12.2
I suggest you to try older x86_64 drivers and it that doesn't work you may try older 32bit ones ( I currently have 9.2 working with slackware 12.2 with no problems but I couldn't install newer ones). It is supposed to work.