It wasn't clear from your initial post that you weren't using the switchbox type adapters, and that's what people often use. They don't work very well.
If it's an internal problem, then it could be a broken chroma (color) signal. This could be checked if you have a multimeter.
This shows where the chroma signals from 2600 (TCOL) and 7800 (MCOL) are mixed together, until they reach the RF modulator. If it's internal then the problem would be somewhere in here, since it's happening in both modes.
R16 and R17 are in the upper left area of the board. To find these resistors, load up this site:
http://saundby.com/atari7800mod/7800...struction.html
They're shown as "2600 chroma" and "7800 chroma" if you scroll down about 2/3rds of the way.
The resistors themselves should have a resistance of about 4300ohms (R16) and 4700ohms (R17).
The top side (the output) of each resistor should have continuity to each other. This is where the chroma signals mix and head towards the RF modulator.
Check the resistance between that point and the metal RF shield (ground). It should be around 400-500ohms. If it's much lower then R2 could be bad.
On the schematic, R2, L1, and C8 could all potentially break the chroma before it reaches RF.
L1 is between the RF modulator and the 2 transistors. On my machine it had a couple ohms resistance across it.
C8 is a small capacitor, I don't know any good way to test that with a multimeter.
Make sure the pins going into the RF module are intact.
The RF module itself might be bad, I don't know if those fail in a way that removes the color.
The full 7800 board schematic is here:
http://www.atariage.com/7800/archives/schematics_ntsc/