This is a question about my daughter's pc so I'm not sure what other hardware is installed, but when it is switched on the screen just displays the Win Fast logo with two options at the bottom of the screen - TAB (sorry can't remember what should happen if you press TAB ) and DEL (to enter setup)
Whatever keys are pressed nothing happens.

The keyboard in use was a remote one and did have flat batteries, but we've tried both replacig the batteries and also plugging in a straightforward keyboard but still nothing seems to work.......

any clues?

It sounds as though the system isn't receiving any input to act upon.

"The keyboard in use was a remote one and did have flat batteries,..." (I anticipate you mean wireless.)

Ensure the batteries are installed with correct polarity, and that there is no potential radio/EM interference generating entities near the actual keyboard (transmitter) or the receiving end. (Things like too close to the monitor, desktop speakers, etc.)

I have yet to tinker with a wireless keyboard, but it may be that the standard (PS2) keyboard "support" may be disengaged in the bios. (To free up IRQ's etc.) If this is the case, you'll need to get the wireless running to enter the bios. (Unless of course you clear the cmos by either removing all power and the motherboard battery, and/or shorting two pins/solder points on the motherboard.)

The motherboard manual should have the instructions on the proper procedure to be used to perform this. Some motherboards require you to power the system for two to five seconds during the pin/point shorting. Check the manual.

I'm scared now!
I swapped the batteries and can see the wireless receiver box the lights of which flicker when I press keys on the keyboard.........

The prospect of taking the pc apart and fiddling with the innards is beyond me, I guess that it's going to have to go to someone who is accustomed to such tasks....

What is the make and model number of the wireless keyboard?

Is the PC a proprietary system? (ie; Brand Name - IBM, Dell, Hewlett Packard, Gateway, Compaq, etc) If so, what is the make and full model number?