Remotely turning on/off network computers

We are trying to keep all our computers up to date in terms of Microsoft patches and anti-virus updates. We're running into problems because users aren't leaving their PCs on when we ask them to or they leave programs running that interfere with the patching/updating process. Is there a way we can help this process go smoother?
Via the Internet

One way to do this requires that all workstations be equipped with Wake-On-LAN (WOL)-compliant network cards. Just about any computer made in the past several years is probably equipped this way. You can tell if it is when it's plugged into AC power and the network, but isn't turned on, and you see some type of link and activity lights blinking. You can also check the documentation that came with the PCs. Some changes may need to be done to the BIOS setup on the computer to allow the WOL function.

The next step is to get a program that is capable of generating what is called a magic packet. WOL-compliant network cards are always looking for a specially-crafted packet to signal them to power up the computer they are installed on. The main thing this packet consists of is the MAC address of the network card in the workstation you want to turn on. There is quite a bit of information on this on the Internet that you should be able to find via Google or other search engine.

On smaller networks using hubs, you should be able to send the magic packet and get things working quickly. Switched environments may take a little more work. Depending on the switch you're using, you may need to enter a configuration command or two that will allow the magic packet to pass through the switch on to every port on the switch and to other switches on your network. If you don't have a network protocol analyzer already in your bag of tricks, see if you can download a demo version from one of the vendors that have such a product available, such as Network General's Sniffer, WildPackets' EtherPeek NX or one from the open-source community Ethereal. In a switched environment, you will need to see the magic packet both on the source segment where the packet is being transmitted from and on the destination segment where the workstation that needs to hear the resides.