When I'm om the internet, my computer starts running very fast with a lot of noise, like it's overheating. Is this dust causing this to happen or is it something else.
Also (this is a Dell desktop) every so often I need to pull the power cord and wait 30 seconds before plugging it back in so that Windows 7 can start. What gives with this? Thanks for any help you can give me

Is it still under warranty?

Most computer systems scale their processing power to the need of the computer. If you're idle your processing might be running at half or quarter speed, when you're doing something intensive, like gaming, it will be at full power. This generates heat and causes your fan to cycle up to deal with the added heat and keep your processor cool.

So the quick answer is that your computer is under heavy load. You need to figure out what that is and either remove it or reduce it. You might need to do a factor restore on your computer. Are there any more details that you're comfortable with providing? Age? Model? OS? Processor/memory specs?

Craven is correct. The more you do on the computer, the warmer it gets and essentially the faster the fan runs. If this however is a new issue, it could be related to a virus, eating up resources, especially if this happens on idle; adware, generally targeted towards browsers, causing your browser to eat up a lot of memory, try disabling extensions/addons and toolbars; or a hardware related issue. Often after a computer is a year or two (or older) the thermal paste will have tried up, not always an issue but a vibration could loosen it causing poor thermal evacuation, furthermore, the issue may also be related to the power supply depending on how the system is configured, tends to overheat until the machine is forced to power off, especially when utilizing media applications.

As far as unplugging it to get it to cycle on, there are two common issues associated with this. In some areas there are static electricity problems, even in grounded connections, which cause a build up of static electricity in the computer, as an overload safety, the computer will not cycle on until that energy has been depleted (disconnected for a while will allow it to deplete). The second issue associated with this behavior is a failing capacitors. When they become bulged, or leaky on the motherboard they tend to cause the computer to behave erratically especially upon start up.

If you are comfortable with making changes to your system, I could suggest some tools to help determine that this is not maleware/adware/virus related, and maybe even solve the issue.