Sounds like you're having the same problem I was with my Scoob.
In the starter solenoid assembly, there's a plunger with a copper disc on the end. When you activate the solenoid, it's driven down ~1/2 inch, where it hits 2 copper contacts. One contact should be attached through the starter case to the power wire, and the other one makes a connection to the starter motor.
I
Looks like __I __, where the I's are the plunger.
The 2 contacts are joined by the copper disc on the plunger. When the contacts/plunger wear down, it no longer always makes contact, and it happens all of the sudden, because the power arcs, arcs, arcs as it wears down, then each arc wears and corrodes it more. So you turn the key and get the solenoid click, but it doesn't connect the power to the starter, so you get nothing. You try it 8 times, nothing, then try it a 9th time, and it fires right up. The temp fix is to turn on all the accessories in your car, and leave it in the On position for 15-30 seconds before you start it; the juice circulating slightly warms the contact, making it more likely to complete the circuit.
As for how to fix it, pull the starter. It's probably going to be a nippondenso, but even if not, pull off the solenoid cover, the plunger slides out and you'll see the 2 contacts. Replacements cost me $5 at a starter/alternator shop, and I just cleaned up the surface on the plunger, and wala, no more problems, and it only cost me $5
Drove me nuts too, but that's where I'd start if power is going to the starter but it's not turning over.
Hope that helps.