Optimistically, you could hope it's just the connections of the mode selection knob? Might explain the resetting behaviour and then deteriorating into not turning on at all. I'd have a poke about at that with a multimeter on its outputs to see if anything was obviously up with it (probably will entail damaging/breaking bits of the thing to gain access). As frustration mounts, possibly look to 'hardwire' hack/short it out to fan oven mode permanently if that's feasible (and assuming the other modes aren't important to you). Next stop, get another off gumtree the same size, swap in and throw the old one in the sea or, for added irony, burn it. UKC geeks probably have some better ideas...
