Graphics drivers do not cause systems to not power up. I'd check your connections first, then uninstall the older drivers later. But Joga is correct, the system loads drivers up at the beginning of startup, and this may be causing your delayed startup.
If you want to try and remove these drivers:
Start menu > Run > cmd > set devmgr_show_nonpresent_devices=1 > exit cmd prompt
Afterwards, go into the device manager, choose View > Show hidden Devices - remove the ATi drivers.