No H/W, No Heating - No Hot Pipes from Boiler - Boiler Bust?

[johnnyl]

I turned my heating on last Friday to help dry a few clothes, and noticed no heat in the rads - cue investigation:

Room thermostat - all OK
Other rads - all cold
Boiler - all working and lights as expected, including pilot light on
H/W + Heating Timer - all working OK
Boiler - pipes from boiler are cold
Cylinder - all pipes that should be hot are cold i.e. from boiler and to H/W
Cylinder - pump turning (unscrewed and stuck a blade in to verify), motorised valves working OK, thermostat OK (turned thermostat on cylinder to min and motorised value clicked in and boiler stopped)

I ran the HW taps later that evening and noticed the temperature wasn't as high as normal. Sat morning and the water is cold. This all makes me think something isn't right inside the boiler (heat exchanger, thermostat?). Additionally, the boiler used to fire for a few mins, then stop, then fire again etc - now it just constantly fires and doesn't cut out.

I've used the built-in immersion heater on the cylinder (indirect system) to get hot water, and that's working fine.

Boiler is an Ideal Turbo 2 (condensing), which Ideal tell me they ceased producing in 1995 (the 1980's sounding name gives it away really!)

So questions to the experts:

i) does this sound like a boiler problem? I'm more than happy to replace it rather than chuck good money down the drain
ii) Would flicking the rads on cause this, or coincidence? i.e. HW was absolutely fine before I put the rads on (first time for a few weeks)
iii) I've got British Gas coming round Thursday for a chat as I want to do this 'right' - are they a waste of money and better local people out there? (I'm in BR6)
iv) How long does it typically take to heat a cylinder from the built in immersion? I guess it depends on the kw of the heater, size of cylinder, and temp of water when you turn the immersion on - but ballpark?

I'm certainly no expert, but no novice when it comes to DIY and stuff - I just want to be sure that the problem is definately the boiler before I replace that

TIA.