Help needed …. Intermittent fault where the car wont start.

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I have no idea when it comes to the workings of the Elise so I wondered if anyone on here had any ideas where I should start looking. I have an annoying intermittent fault which has happened twice now in say the last 20 times I've used the car. When I try and start the car it turns over but sounds really strange, like a throaty sound, then cuts out. It will do this for as long as I try. However, if I wait around for 20 minutes then try again it starts straight away??

Car is a 2001 Elise S2