... or: Flashing bootloader again, if that might have gone wrong in spite of the fact it said it was successful.
Starting from the beginning: I tried to flash an Arduino bootloader on an ATmega328P using the setup in picture 1*. Using Arduino 1.0.1, I uploaded ArduinoISP to my ArduinoEthernet, installed the capacitor, then choose "Board->Duemilanove w/ ATmega328" and "Programmer->Arduino as ISP" and then flashed. This was said to be successful (while I got an error when I removed the ATmega from the breadboard - just to check how it looks in case it goes wrong).
Then I changed the setup to picture 2 and hoped to be able to upload a sketch (while keeping the setting "Board->Duemilanove w/ ATmega328"). Unfortunately, I get an error "avrdude: stk500_getsync(): not in sync: resp=0x00". Any ideas?
* Nearly: I am quite sure reset was connected to PIN10 at the time I flashed. I pulled it out later before I remembered to take a photo.