Originally Posted by SilverBack
... ofcourse network cards would not work.
Although network cards can remain active to some extent when the PC is otherwise turned off. That's how Wake On Lan works. The network card is kept at least partially active to listen for WOL packets. That doesn't make what the OP suggests possible though of course.
If what the OP is after is a way of dealing with downloads that take a long time without leaving their PC on all the time using a lot of power, there are a variety of very lower power devices (I'm thinking 10 watts or less) that either ship running Linux or can be made to run Linux. Along with a decent sized flash drive or even a 2.5" or 1.8" harddisk, such things are ideal for handling tasks such as slow downloads.