Decided this needs a trophy as I think I know what it is
I had this problem also, and spent weeks (and some money with Bell and Colvill) trying to get it sorted - to no avail.
Eventually I found that a fellow sprinter (Simon Thornley) who hasa megaK in his Westfield told me hte secret.
Basically, the battery specced in the Exige is too small (bear with me on this - it’s going somewhere) - the Elise specs a 063 battery, which is itself smaller than MG recommend for the MGF - then the Exige has a higher compression ratio than the standard engine (11 rather than 10.5) - which means the battery should be even bigger, but isn’t.
Now, on the K series, there is a crank sensor - the wierd way that the ECU is written means that when the ignition is turned on, the ECU allows the cranking relay to operate, but not the relay which controls the injectors or coil pack. These are not switched on until the engine has got a satisfactory response from the crank sensor that the engine is turning over fast enough.
All seems OK so far - however, if the engine is slightly slow - which could be your battery just a tiddly bit under full charge, then the engine does not crank quick enough and the crank sensor throws a wobbly and refuses to tell the ECU to fire anything else up - hence the cranks OK but no spark or injectors.
Most people tend to let go of the key, leave it a bit and try again - here is the problem - the ECU does not reset until the ignition is fully off for at least 30 seconds - therefore just getting back in and trying again without the ignition having been turned off will not help.
Then you kick the car, go inside for a beer - go back to it the next day and it bloody starts, purely because the engine might be cranking just a little faster. Truth is, had you just turned off the ignition, left it for 2 mins and come back it may well have started anyway. Seems that Exiges are right on the threshold speed to crank - sometimes it just doesn’t get it going fast enough, and you can never tell when that will be.
Simon from MG confided in me that they have ECUs in Rover which are modified with a green LED and red LED that tell them visibly whether the engine is cranking over quick enough if they get a problem on the production line - that’s how common it is even with the correct battery.
With the standard battery, you will never fix this problem (assuming your Exige suffers - some have less volt drops in the electrics and will never be afflicted)
My fix has been to fit a bigger battery an 065 rather than an 063 - gives 520 amps of crank instead of 340. The only problem is that it is 1 inch bigger in the left to right dimension when looking down from above. It is possible to fit, but bloody difficult - basically you have to pull wiring as far out the way as possible, remove the radiator shorud and then remove the 5 bolts holding the heater in place and slide the heater as far to the left as possible. Then you can JUST squeeze the bigger battery through the gap by tilting it - once it’s in it has plenty of room as there is clearance on the floor under the chassis leg, so the heater can be put back into it’s normal position. The battery clamp has to have the right hand edge removed to make way for the wider battery, but once it’s in, it’s in and will not go anywhere. Since then, job done, no more starting problems, and a battery that sits for weeks longer before needing a charge
Sorry for the long post