My a/c button does not light up but it works fine, been that way as long as I've owned it.
With the engine running press the a/c button, do the electric fans behind the grill come on?
There are two, they both should come on, if not it might be a...wait for it...blown fuse.
If the a/c is so low the compressor will not kick on you need a shop to trick the compressor so they can fill the system.
I was taught a trick to fixing leaking a/c lines, where the metal line crimps to the rubber line you can clamp the collar with a really good hose clamp, that will stop the leak.
That is the most common place for a/c leaks on older cars.
The a/c on the DI will run no matter the outside temp, I've ran mine at 0*F to defog my windows in the winter from breathing to heavy after sledding.
2nd owner of a '97 Disco with a ARB winch bumper, SD roof rack, Rover Racks ladder, Cooper S/T's and 220,000 miles on the clock and still a daily driver.