Is A.I. Dependant On Hardware or Software?

It's a simple question. There must be a point at which A.I. cannot become a reality unless 1 of these 2 exceeds todays standards:

Software: We are told that machines need only be constructed with sophisticated components, then eventually they will develop A.I. The question is whether software is more important than the hardware. For example can you actually develop A.I. for a PC of todays type using extremely futuristic software to aid you? In theory it should be possible to run a computer of today and have it be self-aware, after-all people don't use nearly as much processing power in their brains. That begs the point, perhaps A.I. is only limited right now because software developments are too!

Hardware: This is the holy grail of science, the better / faster your hardware the more chance you have of producing something substantial. The reality is that without great software to make it run there isn't a point to have a 5 GHZ computer! Hardware can only take us so far before A.I. will develop, and it's at that point where software must exist in order to run A.I. So do you think using todays technology we might be-able to construct an artifical intelligence on par with our dreams?

If written in the right way would software allow A.I. to develop on your home PC?

Comments and arguments welcome.