Try this. BTW, there are actually three cables. There are two others; one from the junction box to the left latch, and another from the left latch to the right latch.
If the chime annoys you, it can be unplugged.
Replace hood cable
From rsmillar
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It depends on where the cable broke - there are actually two cables used to open the hood. One runs from the handle, thru the firewall and under the driver's cabin air intake, snakes around to the driver's inner fender, to a "junction box". This is a clever little plastic piece which snaps into the fender, and houses the junction between this and the next cable. The next cable runs on out to the hood latch.
Mine broke right at the handle. It took me about 30 minutes to replace it, and the cable was $12. Hardest part is gaining access to the handle - you must remove the "dead pedal" trim piece, which is sort of a PITA. Other than that, be very careful when unsnapping the junction box else the snap will break off.
Remove the inner trim piece (the "dead pedal") and you will find the end of the broken cable. You'll very likely be able to grab the frayed strands of the cable end with a pair of pliers (make sure NOT to grab the outer (black) housing) - then simply pull and the hood will open!
To get the trim piece off, you first take the piece off from under the dash - as I recall there are 4 screws and three quick release connectors. Careful about the chime - it is snapped into this piece and includes a wire harness. Just remove the trim piece and set it off to the right, next to the center console.
Next, go to work on the dead pedal panel. Remove the release handle (one screw, IIRC) and then I think there are 3-4 screws holding the panel, BUT it also has a large plastic "foot" which supports it against the firewall. Spend some time working this out, or you could crack the plastic (you'll see what I'm talking about when you get in there).
Once this piece is out, as I said, you will have access to the broken end of the cable.
This gets the first trim panel off (don't forget to first remove the piece of trim carpet off the center tunnel - it just slides off towards the rear of the car).