I have a Toshiba Satellite L450-O3D. I would like to find out if you can keep a live connection with the internet during sleep mode. I've already tried opening Device Manager and unchecking the box that reads, "Allow this device to turn off to save power" for both my router and modem. My router model is a Cisco WRT-310N.

"keep a live connection with the internet during sleep mode" If the system goes into Sleep Mode generally you're going to have the HDD & other parts of the system powered down, but you'd still have the ability to access discs remotely (say through a VPN) after they spin up b/c the internet connection should be up. You'll want to look at devmmgmt.msc and look for the network adapter section, double click it & choose power mgmt, make sure the option 'allow the computer to turn off device to save power' is unchecked. If that doesn't work you'll want to check your systems BIOS settings.