Hmm...i doubt it is spyware or something, and seems more likley to do with drivers or the connection taking valuable CPU power since its connnected and sending out and recieving back data.
I doubt your ram is anything to do with it either, since that should be fine.
A good card for internet usage shouldnt use CPU power hardly at all since it'd be built to handle this type of thing on its own.
By any chance is it a card built into the motherboard as it were? Or is it an external card you got given with the internet connection when you bought it?
If its a card thats built into the motherboard, you might have found your issue, and might be best to buy a DSL board that will fit into a PCI slot and allow you for internet access (talk to your Internet Service Provider)
If it is an external card, then i'm stuck as it shouldn't be using that much resources...
I hope this helps