Hello and welcome.
I strongly suggest you do not continue putting the Mac in the freezer and then powering it on. When it is removed from the cold temperature, if it is not left to come up to room temperature for the proper amount of time, you could end up causing more damage to the internals, or cause an actual fire. If there is any residual condensation on the logic boards and/or in the power supply itself, powering it on could cause a spark or short, and the LCD panel is not built to withstand this type of treatment, which could lead to discoloration in the panel itself.
My guess is that the internals of the base aren't being cooled properly by the fan during operation because the vents are clogged with dust (a known issue with that model), or simply some of the power supply components are failing due to age. It could also be the PRAM battery, if you are experiencing any issues with the clock resetting and not displaying the current time after a power down. Since it won't power back on after shut down, it could also be that the thermal paste has dried and isn't making contact, which would prevent a kind of thermal lock until it cooled down enough to make contact. Because of the unique construction of that model, it is NOT a user-serviceable Mac, and only qualified technicians should attempt to troubleshoot/repair it. There are a couple of disassembly/assembly steps that should be performed in the proper sequence, and require non-standard tools for proper torque.
Bottom line, it isn't safe to continue your "fix" procedure. In addition, because it is going on 13-14 years old and running Mac OS X Panther 10.3.9/OS 9.2, I am sure you are having more difficulty using it successfully on modern websites and cannot update any of the software you may use on a daily basis. Unless you can find an Apple Authorized Service Provider that is willing to take a look at it, I would just retire it and replace it with a newer model. Even if they could determine any faulty parts, they are officially discontinued and can be very hard to find and expensive.
C