I had the same thing happen to my 2000 Camry LE. If you pulled up on the latch nothing would happen. If you pulled up on the latch and put pressure on the latch towards the passenger seat the trunk would then un-latch.
I decided that the cable had stretched, so I figured I'd tighten it up. Only problem is that there is no adjustment.
I removed the cover of the latch by the driver seat but no adjustment. To get to the mechanism I started to remove the plastic trim thingie on door sill, and then saw I'd have to remove the carpet. Then it looked like I'd have to unbolt the seat and remove it to get to see more of the mechanism. Screw that.
I'll go to the other end, I said to myself.
So I open the trunk, and the latch is under the ever so stylish custom molded el-cheapo deluxe cardboard cover held on by about 20 plastic push plugs. So I get the cover off, and I can see the latch mechanism but there is no adjustment for the cable.
The cable is terminated with a lead ball to keep it in place, and there isn't any place to put one of the screw on cable clamp shortner gizmos. Fooey.
I figured a beer might help so I opened one, and sure enough it came to me. Since I couldn't easily shorten the cable, I'd just shorten the length between the ends. I got a 10-32 nut, put it in the vise, and sawed through one side, so now it looks like a "C". I slipped the open end of the nut over the cable in the trunk, right next to the ball that was crimped to the end of the cable and squeezed the nut shut with a pair of pliers. That shortened the cable by 1/16". I hooked everything back up to the latch in the trunk, and it worked better. I sawed another nut and added it to the cable, and that shortened the cable a little over 1/8" and it works just as it should. Out of pocket costs, two 10-32 nuts, and a few minutes with a hack saw.
The easiest way would to have been to get some split shot, the kind they use in fishing, but I ain't a fisherman so I didn't have any, and I didn't want to drive to the bait shop to get some. I'm not too sure how long the split shot would last, or if it would come loose under pressure, but the crimped on steel nuts will last forever, no problem.
As it turns out, I mangled up a couple of the plastic push plugs that hold the ever so stylish custom molded el-cheapo deluxe cardboard cover in place, so I had to go the the hardware store to get some to replace the ones I screwed up. As I left I noticed the Fishing Department, and was temped to pick up some split shot in case I had to shorten up some cable some time in the future. But I passed on that idea.
I kinda like the "saw the nut in half" method.
So maybe this might be the answer to your problem.