Plug your 360 drive into the motherboard inside your pc via sata. If you have a laptop might as well forget it with out additional hardware.
Well then to use that computer you would need to purchase a x360usb and if you got one of those you could then flash your drive from any computer.
...also when you say "Philips" is it a BenQ or LiteOn? A LiteOn will need a probe III. Get someone to do it for you if your going to have trouble.