When I did it about a year ago I used HRD plus a toggle on the appropriate interface line on the DB15 plug to power on and off the K3. I used a relay controlled by USB.
There are plenty of interfaces available, all you need to do is write some simple code in C++. Many of the EBay interfaces come with limited software but they frequently use the HID interface so you can write your own control software. If you don't want to write code try and find one supported by amateur radio software, these tend to cost more. If you want to go that way look at the LP Remote.
The Modtronix Ethernet boards are very good for remote control as you have a web interface and can also monitor voltages etc. It means you do not need a PC left on and if your PC crashes you can reset it with a relay across the reset switch. WW2R has written code to control his, mine is still in the projects stack.
Velemann do a popular USB interface kit, the K8055 for about £25. This requires a PC to drive it but you get 4 relays and plenty of digital and analogue IO ports. Many people have written software for this unit, me included. The kit comes with a disk with sample code and a DLL to interface to.
Finally, there is always the PC printer port, if you have one. It is the simplest and lowest cost method and you can drive it directly from popular radio control software.
Mike