Water leaking into

Hunting water leaks is a pain in the tailbone job to do. I'm assuming yours has the jack in the floor of the trunk, under the carpet.
The spare wheel well is the lowest point in the trunk so the water will collect there regardless of where the leak is. Start with the simplest tools, a flash light and the palm of your hand.
How much water is collecting and how fast does it fill up? Rain water coming up through the floor is unlikely unless the floor is damaged.
First take everything out of the trunk that wasn't in there when it came out of the factory. Take a really good look at the carpet and trunk side liners. Use the palm of your hand and feel the floor carpet for wetness. Your feeling to see if it is wet in a particular area. Using the flashlight look for darker patches as carpets often darken in color when wet. Move to the rear of the trunk and feel the liner on the back of the rear seats. Next run your hand over the side panels where the wheel arches are. This will give you clues as to where the leak is possibly coming from.
If the whole trunk carpet and liners are bone dry the leak is from under the car.
All the doors, the trunk lid and the sun roof are fitted with rubber seals to stop rain and road splashes getting inside the vehicle. Over time these perish and start to leak. Run your hand around the underside of the rubber seal the trunk lid sits on when closed. This is the most obvious place it will leak from. You can do this on each door as well because water can travel a large distance before it finds somewhere to create a puddle. A Sunroof can also leak but they tend to cause puddles in the foot well.
If you get a few dry days you can test for leaks with a hose pipe. Keep the trunk closed and make sure the inside of it is totally dry. Remove any spray nozzle from the hose so it flows at regular pressure. Carefully aim the water so it only flows over the trunk lid. Let it flow for a minute or two trying not to soak the doors at the same time. Turn off the water and leave the car alone for about 10 minutes. Wipe off any excess water on the trunk lid, open it and see if its now wet inside the trunk. Yes? the trunk seal is leaking. You can use this method for the doors and sun roof as well. Door and trunk seals are usually just a 'Push on/Pull off' fit so you can easily change them yourself.

Hey Grady..
There are few things that could cause the water intrusion... Is the carpet in the front floorboard wet?.. ..Has it rained recently? This will rule out window seals leaking? Have you opened the trunk and checked to see if water is in the trunk? OK..IF it has not rained, no water in the trunk, AND the front floorboards are wet, then the heater core is leaking...
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Grady.. sounds like its either the window seals or the door seals.. check for damaged door seals, cracked window seals..

Sounds like the door gasket or trunk gasket is not sealing.
You may have to take it to a body shop to find the problem.

Easiest way to figure it out, toss a friend in the trunk with a flashlight and grab a hose.
Pour all around the seal with the trunk closed, wouldn't surprise me if it's worn or falling off considering you're having trouble closing the trunk as well.
Do the same for all the doors, sunroof if you have and windshield .
Those seals normally aren't hard to replace and an easy way to make sure the new ones don't leak is to grease them before winters, some white grease works well, not the prettiest thing but it keeps the rubber from freezing and cracking.

When diagnosing a water leak, here's a handy tip. Check the accumulated water. If the water is dirty, look for leaks from the underside of the vehicle (floor, wheelwells, etc). If the accumulated water is clean, look for leaks from the topside of the vehicle (trunk seal, window seal, etc). To find where the water is coming from, shut yourself in the trunk with a flashlight and have an assistant run water over the trunk with a garden hose. You may have to remove some of the interior trunk trim to see exactly were the water is coming from, but chances are you'll find it. Also another common cause of water leaks are from impact damage, so check for collision damage repair. while your in there. -hope this helps.

The green solution is Radiator Fluid. There is a leak from the Heating / AC somewhere. Since you have already checked the Heater Core then the likely culprit is a loose, cracked, connection or hose or line that has a hole. And because of the heat generated, they are hard to detect because the leak "dries-up" before you can detect "where".
Because of this: re-expose the Heating / AC system again = take the dash components back off. You can reconnect the electrical components that turn-on and run your heating controls. Use dry, white paper towels wrapped completely (from one end to the other end) around the hoses/lines. Start you car and run the Heating. The paper towels will not dry as rapidly as the lines will. The wet towel section is the culprit and the one that needs to be replaced.
Let me know if this helped, or if you have additional information or questions. Feel free to contact me at FixYa.com!

Sounds to me like your issue is with condensation from your air conditioner. The condensation isn't properly draining, probably from a damaged or clogged drain hose.

I had a similar issue and found that the two rear drain holes for the sun roof came off and any water was running down into the trunk and also the rear floor was always wet. I pulled the rear of the roof panel down to expose the rubber tubes, re-seated them with glue so they would not come off again.

I am the original owner of camry xle 1998 with wet floors. In 2000 I had drivers side door seal leaking at welt. Removed old door seal and new weather strip on drivers side installed. The door panel was never wet, but wet at bottom of door where there are drain holes...slowly leaking under carpet.
In 2001 later water again. Coming from overflowing A/C evaporator-drain plugged/ tank full of debris. Removed evaporator, cleaned + drain cleaned.
In 2003, driver door seal against window rotted. Removed door panel and found leak at window belt molding at the mirror joint inside + out. Lots of mold under carpet needed to replace! Made a fuss at dealers for reacurring problem and they replaced the carpet for free.