Arduino Uno and Ethernet Shield not powering correctly?

I have a Arduino Uno and a Ethernet Shield using the standard Ethernet.h library. The board has a dht 11 module and a photodiode for reading a power meter connected as well as a analog NTC temperature reader. All of these are supposed to log its content to a thingsspeak channel. I have also connected extra capacitors for providing extra power to the board. I also had a I2C 2x16 display connected but removed this because of suspecting power loss.

This config works fine when connected to the computer. When I remove the computer connection and plug the usb cable into a usb charger it works half of the times. rest of the times the ethernet diodes are not lightning up. If I use a separate dc adapter I can also get it working by starting it and then pressing reset after a few seconds --> the ethernet shield lights up and connection works (9 volt 450 mah). When I go to the power meter and connect the board there to the same adapter but to a longer ethernet cable - It just won't start the ethernet no matter how many times I reset ut. The board only got 2 diodes let and just won't go live with the rest. I have also tried other cables closer to the router.

What should I do next..? - Connect stronger 3.3 volt adapter directly to the 3.3 volt slot in order to power up the shield better? - connect stronger adapter to the arduino uni power connector? - Could I have done anything wrong in the code that might affect powering options (it ALWAYS works when I connect it to a computer via usb only? - Other tips?

Sounds like an inadequate power supply. Connect a multimeter between the arduino 5v pin and arduino ground, then try your various power setups and see if the arduino 5v pin maintains ~5v.