That the charging circuit looks to be just a few parts. You swapped battery and wall charger so the last bits are the motherboard and that's about it. Get an estimate for a new mainboard.
But it looks to be over 4 years old so I'd start shopping.
I am at the end of my known troubleshooting options. Here is the issue: i have a Toshiba A665-S5187x satellite. I was typing away one day when a message appeared that told me my battery was low and to plug in my power supply. Unfortunately, I was already plug in and in a couple of minutes it shut down. I tried to turn it back on, the switch light came on, and I could here the fan start and then it immediately turned off. The power led was on but the orange charging light would come on for approximately 7 seconds and turn off for 7 seconds. It would repeat this cycle about 5 times and then flash twice and begin the cycle again. The following were the troubleshooting steps I took:
1 I pulled the battery and unplugged it from the power supply and did the whole power cycling thing.
2 Replaced battery
3 Checked the voltage of my power supply.
4 Tried to start it with just the power supply connected.
5 Pulled the memory and replaced it with known good memory
6 Replaced motherboard with a new one, including new power jack.
Have I missed something?? The only thing I have not replaced is the processor.