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Timing belt is a good possibility. They often decide to loose their teeth on startup. The engine would in most cases crank over differently than when the belt was correctly timing the valves. Compression would be lost, so it would crank faster.
Second thing is spark. Get a spare plug, and connect the coil output while laying the plug on a grounded spot. Cranking should get you sparks. You might want to also check the relay that powers the computer, and maybe listen for the injectors ticking. But I think that the fuel pump priming indicates the computer has juice. Check the grounds on the coil too.
tom
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