Does cable internet connection stay on while computer is in standby?

I have recently connected my 2 computers to a router so that they could share my new cable internet service.
I like to leave my computers in standby but I am unsure of the security risks. My question is whether or not my internet connection stays active when they are in standby. I'm thinking that the connection is NOT active because when I wake them from standby the little systray icon pops up a message that says something like "LAN is now connected".

I don't have any vital info on my computer but I just want to know if standby is a bad idea now that I am hooked into cable, where the internet connection is always "turned on". When I was on 56K dial-up service I did not have to worry about this.

As always, thanks for replies.

Wedge
 
standby is a pretty useless feature that should really only be used with Laptops/notebooks (to conserve power consumption for them *as being they are on batteries). It actually creates more problems on desktops sometimes.
You kinda answered your question yourself, but sometimes also, some companies when they don't get a feedback response from your LAN card, they disconnect you until your LAN card starts sending little packets back again.
 
It should be safe in standby mode - considering almost everything is powered off. There shouldnt be any network activity from a computer in standby mode. To be safe make sure wake up on lan is turned off in the bios.
 
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