Should have bolts on the underside or on top of the rad support on the hood latch. But you could try using a flat punch or 1x1 to knock the hood catch to align it with the hood release. If this doesn't work, then of course you need to replace the hood release.

The cable is rubbing on the insulation and isn't able to retract. Routing of the cable is through the firewall and clips along the driver's side fender and rad support.

 

There’s also a supporting rod that goes towards the lower front of the rad support and if it’s bent it won’t align your hood properly and you’ll struggle closing it. Both easily removable items from the junkyard mine was bent front a mild impact and now my hood feels nice and tight

 

There are three bolts holding the hood latch and there is some space for it to be adjustable. The cable has to be taut or it won’t open, there are a few corners it has to run through, like around the battery.

Is the latch still functional? Maybe it just needs to be cleaned, especially the spring.

Years ago my hood wouldn’t “pop” and sometimes not open at all. I made the cable taut, adjusted the latch, cleaned it with degreaser and lubricated it. Now it works like new.

 

is it dry to the bone or lubed up good?

 

It's pretty dry. I unhooked the large spring in it and then reconnected it, and no something is hung up. I'm just going to go to the junkyard and get one.

 

Just got back from U-Pull-&Pray - it's only three miles from where I live now - and got me a hood latch, the cable, and the release pull. So that should get my car fixed up. I also got a window switch bezel since I broke the tab on mine when I last had the door apart... I also got a proper gas cap for my 2005 Mustang and an AM/FM/Cassette with clock from a '96ish Windstar for my truck. Total cost? <$36.00!

The latch wasn't bad at all. Three bolts and it was out. I did remove the grill to access the lower bolt, but on my car I will see if I can avoid removing the grill. The cable seemed to want to stay with the latch, so after removing the plastic inner fender liner and disengaging the other end of the cable from the release pull, I snaked the cable out of the cabin and finally out of the fender apron and upper radiator support. Then I removed the two screws and took the release pull, since mine is now bent.
Maybe tomorrow I'll try putting it on my car. I think my cable is OK, so I'm going to try to use it, since it doesn't look fun getting a new one fished in there - especially once it enters the cabin just inside the kick panel/toe board/firewall area.
The Donor car, a '93 with manual windows like my old one, had some white plastic deal with relays or something electrical, which was right in the way. It had a lower bolt which I removed, but seemed like it was secured at its top, deep up into the dash. (I didn't pay enough attention to it to describe it better - my mechanic's tunnel vision was focused on the cable)

 

Did you check the fuel tubing under there at nylon brass juncture, maybe no crusty! 💩

 

Didn't look, but I am in the rust belt for sure, so you surely ain't missing anything.

 

Today I put all three parts in/on my car! I started by removing the latch, and when I did, I could see that the cable was in bad shape. So I sighed loudly, and removed the battery, left front wheel, and plastic fender liner. Then I fished the old cable out of the car with the old latch. I also removed the release/pull handle from the dash. I ended up removing the grill too, since my socket wouldn't fit through the Toyota medallion.
Then I snaked the new cable under the top of the radiator support and into the fenderwell. I then popped it through the grommet into the cabin - and when I got in the car and looked, I could see the cable hanging there. So I engaged it back into the release/pull and moved the release into its hole. Then I routed the middle of the cable up over the wheel arch and engaged it into the plastic clips which retain it.
Then I tightened down the latch and used a screwdriver to mimic the loop on the hood, and locked the latch. It popped open when I pulled the release! So I closed the hood, but it took a little more effort than normal, so I adjusted the latch slightly upward - Toyota doesn't give a lot of adjustability to the latch unlike other makes.
Then I put everything else back together, and put in and tightened the screws for the release/pull that I'd forgotten, and called it done!
I also put the new horn relay in, but still no horn. When I went to unplug the connector from the horn, the wire easily broke. I ended up destroying the connector to get the female spade terminal out, and used that terminal to sandwich the bare wire to the male spade terminal on the horn. Still no horn!! So I put my old relay back in and finally it worked!
I finished by putting my new window/lock switch bezel in the door.
Now my Corolla is back to all of the functionality I'm used to.