If you open the hot water taps are you getting water out, albeit cold?
If so, the blue handle on the valve may be worn and isn't turning the internal ball to open the valve. You need to loosen the wee screw inside the blue handle, pull it off and see if you can turn the brass square underneath it to open the valve, with an adjustable spanner or pliers. Careful as you could get wet very easily.
Don't touch the valve in your 2nd pic