Power Management

If you instead put your computer to sleep then whatever program you are using to record TV should be able to wake it. Usb mce remotes don't work with a pc that is completely powered off, once again it can work from sleep.

If you built your PC, the BIOS may have wake timers for turning the PC on a particular time from complete shutdown.

Any other approach will involve using S3 (suspend-to-RAM) mode. This is pretty common with modern hardware and you'd most likely want to use Wake-On-Lan (generic term) to wake up your PC and built-in windows power management to put it to sleep again. Windows 7 is pretty good about not entering sleep mode when files are being shared by another device, but there are always quirks.

It's a project for sure and there are a million different ways to set it up.

Depending on the configuration of your PC, you might also be able to use some software to lower it's power draw (via undervolting) while it is on as well, to further reduce energy usage, and lower heat generation.

Since getting your computer to sleep is new to you, I will give a brief summary to get you started. Search the web for details.

The first thing you should know is that you cannot always get your computer to sleep reliably. It may not wake at all, or some things may not work properly after the computer has been sleeping one or more times. Reliable sleeping needs the hardware and hardware drivers to work correctly. However, modern systems are much better, and there is a good chance they will work properly.

The Control Panel is used to configure how the computer sleeps. Go to: Control Panel > Hardware and Sound
Then under “Power options”, click on “Change when the computer sleeps”

There are several power states:
Off: Zero power used. The computer is unplugged, the battery is removed, or the switch at the back of the computer is flipped.

Soft Off: Usually 1-5 watts used. The computer is shut down. Most of the hardware is powered down, but the power switch works. A USB remote receiver cannot wake the computer from this state; you need a remote receiver that is connected to the motherboard’s big power cable. A few motherboards have special headers that can also be used. An example of a remote receiver that is connected to the power cable is:
http://www.newegg.ca/Product/Product.aspx?Item=N82E16811999191
(Note: I have not tested this remote receiver. My HTPC case has this functionality built in.)

Hibernate: Usually 1-5 watts. This state is the same as Soft Off, except that when it hibernates, the computer’s entire running state is written to disk before it shuts down. When the computer is wakes, it reads this data and restores it to the state (running programs and all) that it had before hibernating. Waking from hibernation requires the same special hardware as Soft Off.

Sleep (S3): A bit more power than Soft Off or Hibernation. In Sleep, more of the system is powered. (A power outage while sleeping will crash the system.) The RAM stays on, so the computer can wake in just a few seconds. USB remote receivers, keyboards, and mice can wake the computer, if the power setting in their drivers is set correctly. Wake on Lan (WOL) can also wake the computer. To do this you will need to set the network driver to wake on a magic packet. You may also need to change a BIOS setting.

Hybrid Sleep: The same power as Sleep (S3). This is the same as Sleep (S3) except that it also saves the running state to disk, just like in hibernate. A power outage while sleeping will not crash the system, instead it will wake like it wakes from hibernation.

P.S. There are devices that can turn other equipment on or off depending on the computer’s power usage; they can power the equipment off when the computer is sleeping, and power it on when the computer is awake. I do not know if this could be used with an XBOX.

Don't forget that the BIOS also has to be configured to work with the right sleep settings.

Unfortunately, you haven't posted any info on your HTPC, so I can't really help you setup S3. However, there are plenty of useful info out there for doing so, just google "enable S3" or something similar.

I don't think the HD HomeRun is capable of sending out WOL packets. However, if you configure your HTPC properly, it should come out of sleep mode on it's own for recording and then follow the selected Power Plan to go back to sleep (after 30, 60, etc minutes of inactivity -> Sleep/Shutdown/etc)

My solution is very simple. My HTPC is set to sleep after 3 minutes, but stay awake while using media center. I don't ever turn it off with my remote, I just let it go to sleep. Whenever I send any IR command to it or use an Xbox extender, it wakes up automatically. It also wakes for recordings and guide updates.

You should be able to set up sleep in control panel - power options - advanced, provided sleep is enabled in your bios. You'll also want to turn on the option to have your PC turn back on after a power failure.