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Are you saying the secondary release handle on the latch itself, or the pull handle inside the car to release the primary lock?
OK- The plastic hood handle is forked at the end, and goes around a metal lever with a pin through it (which goes through holes in each side of the fork) then a metal clip holds the two sides of the fork from spreading and coming off the lever pins.
Now- your objective is going to be to pull that lever! You had the right idea with the coat hanger, but you need to make it straight for about a foot, with a relatively tight hook at the end. If the pins are still on the lever you can hook it and pull outward, but if the pin itself fell out (and took the metal clip with it!) then there is nothing on the end of the lever to grab except the hole itself that the pin was located in. You should be able to lift the hood about 2" to be able to access the gap. If the handle is gone you can also remove the trim piece around the hole for better access. If you are using a flashlight you may have to see if you can get a slight angle view into that gap to see if you can hook your rod through the hole in the lever if the pin is missing.
If the pin is missing, and you can't find it, you will likely have to get a new latch, as the pin and clip are not available separately. If you can still find the pin and clip, be careful re-assembling as if it falls out once it will be pretty loose.
Installing a new handle onto the lever is tricky, you have to spread the fork at the end (I use a flat bladed screwdriver and twist lightly (not too hard or you will break it) until it is wide enough to go over the ends of the pin. Release it so it is on the pin, and then seat the clip downward to hold the fork from spreading.