Earlier quoted context omitted.
The cloud significantly lowers capital expenditure to get into an Internet-enabled business, which cultivates the very startup ecology that Y Combinator exists to leverage and support. Those teenagers who started the Facebook Pokemon game would have never had the resources to build a scalable solution with hardware that they own. (That is, unless Y Combinator paid a lot more money as part of participating. They might…
You can do a lot of the things you describe here with VPS (Virtual Private Servers). You get root access, you don't manage hardware, you often receive some virtualization benefits (images, snapshots). Does that count as "Cloud Computing"?
VPS providers give you the tools, cloud providers give you the tools and a few finished products with less flexibility. You can use VPS as part of a cloud implementation, just like you can use dedicated servers as part of a cloud implementation, too.