Remote Access to a computer, pure hardware solution: e.g. virtual lenghting mouse, keyboard and monitor's cable

We've a computer that runs a software, something very valuable.
The software runs on Windows XP and the OS is protected so that we can not install any other software nor change it's setting.
We want to have remote (or off-site) access to this computer and it's software (for educational purposes). As I said, we can not use remote-desktop software bases solutions.
We are looking for a way to have a hardware solution for remote accessing this computer.
Suppose that we want to lengthen the mouse, keyboard and monitors cables.
Is there any hardware product available for this?

As I thought, we could build two hardware devices, one is attached to the target computer (plugging it's cables to mouse, keyboard and monitor) and connecting the other end of this device an other computer that is connected to our remote device, via WiMax, e.g. reads signals from monitor port of target computer, changes them to data, then passing to computer which is connected to our network, then in that computer, a program reads those data, transmits them over the network to the off-site computer, then those data are passed to an-other device (which is the second part of our hardware solution) and that device changes those data to some kind of voltage and passes the to a monitor, and this cycle repeats e.g. 16 times a second so that there is not flicker on the screen. Also mouse and keyboard data are transmitted in the same way from the remote off-site computer to our target computer.

I think this solution is possible, but some how complicated, costly and hard to achieve.

Is there any other alternative way to do what we need? e.g. some existing hardware based solutions...

Any comment is highly appreciated.