Starter occasionally makes grinding noise and does not crank engine when key is turned to START position. Next attempt may or may not reproduce problem. When it reoccurs during multiple attempts to crank, moving the car only inches will correct.

the starter motor on the engine cranks the engine fast.
or does not.
fuel never causes starter motor to fail (unless hydralocked)
car is in Australia or Europe. not USA 1.3L or 1.5L engine.
when you turn the key to run (from off)
the dash IP cluster lights up. and glows many lamps doing the lamp self test. does it?
then you turn the key to start (this is cranking) and the starter makes a loud noise cranking fast on any dead engine,
grrrrrrrrrrrrrrrgrrrrrrrrrrrrrrrrrrrr, (like grinding coffee)
the engine crank shaft even spins fast, (seen by looking)
if this fails cranking there are 6 causes (and tests)_
if engine fails to start but cranks fast there can be 50 causes.
and lots of tests using tools you do not have.
for sure old cars like this., things do fail.

tell what the starter does.
the M/T transmission cars can be push started.
in 2nd gear.

The starter circuit goes through the gear sensor, and possibly other switches. If any are open, current doesn't make it to the starter. If Park doesn't work, try Neutral, as a test. If you can find a location for the shifter where it cranks, that would suggest the switch has come loose or shifted its position from where it should be.
Are there any starter noises, such as the click of the starter when you attempt to start? If a click or a chatter, the battery may be low.

You need to have your flywheel: replaced.Your starter motor engages against the fly wheel at the back of the motor. Every time your motor stops it tends to be in the same few positions (just the way things work) so there is more stress on some parts of your fly wheel than others. Because of this the teeth wear out on the fly wheel which means the starter can correctly engage on the fly wheel which is the grinding noise.

try to jump start it if it starts its the battery,if it doesnt than it time to remove the starter and go have it tested,while its out look for any worn teeth on the flywheel and starter solenoid teeth also.if starter comes back ok then look at all the cables,look for corrosion as it can hide under the wire sheilding.

From what you describe I would suspect that the starter is not fully engaging. I'm assuming that the grinding noise you hear when you try to engage the starter is INSTEAD of the engine cranking. If I assumed wrong, ignore the following:
Pull the starter, check the flywheel for excessively worn areas. Most of the time the flywheel is ok, it's just the starter. Any time you disassemble a starter you should replace the bushings and brushes. Never remove the starter with the battery still connected. Remove the negative terminal from the battery before you attempt to remove the starter.

if the starter is making a grinding noise when you turn the key, it's one of several possiblites. 1. Bad Starter. 2. Bad flywheel. 3. You need starter shims that fit between the starter and the motor. Most starters will bolt straight up but sometimes the gears get too close so you need to shim them apart.

could be, make sure battery is fully charged then have someone hold the key in the crank position while you test for power at the small wire on the starter, if theres power in the crank position then i would say a bad starter, heres a diagram of the wire location.

Your post interested me, as I just purchased the same vehicle lasts month. The grinding noise while attempting to start the CRV sounds like like a problem with the starter 'clashing ' with the flywheel. When you turn the key to start there is , a small gear in the starter on a shaft that advances (moves down the shaft) and meshes with the flywheel (which is a large 'gear'). When they mesh together, the starter gear will spin, and turn the flywheel, which 'cranks' the engine over to start. When a car is old, you can experience a loud grinding noise, as the wear and tear can cause the gears to clash, not mesh smoothly. Since this is an '09, that of course isn't a wear and tear issue, something was not tightened during assembly, or is defective. You MUST bring it to the dealer, to establish that there is a problem, even if they deny it. To continue to drive it could cause damage to components (actually driving it is probably ok, it's the starting it that will cause damage). So, insist that they check it out, you may be surprised by their desire to fix it, and have a happy customer to advertise their cooperation and quick fix of the problem. Hondas are great cars, hopefully this is a rare minor assembly or defective part glitch that will be quickly fixed. Keep me posted as to your visit to the dealer. Remember that you can bring it to any Honda dealer, although I would start with the one where I purchased it. The car is under warranty, get them to fix it, and enjoy your new car.

Starter has teeth that mesh with teeth on the flex plate . most of these type grinding noises are do to missing teeth on the starter gear or flex plate missing teeth .Does your vehicle have a automatic transmission ? Have you had starter replaced lately ?

do you mean engine rolled over or cranked over and would not start?or is it that the starter would just click? or did starter sound like it was wineing and you had to keep on and off the key until it findley started? if any of your answers to thies questions is yes (except first question) its time for a new starter. as far as the grinding noise don't worry about it, that's what makes me believe its the starter. install new starter, problem solved.