I have the A5 with the DVR station, so my set-up won't be quite the same as yours but for me, I connect the OUTPUT cable (scart to composite) to the output on the SKY box (scart) and composite to the input on the DVR station.....I then shove the player on the DVR and it springs to life.....
So first things first - does it come up, like the A5, with the option to Switch to TV out when you stick it on the DVR station? If it does, pres cancel.
Secondly, and not wanting to patronise - make sure the cable going into the DVR station is in the input section.....
Thirdly - if you are connecting to the TV via Scart (if the cables are similar to mine) does you TV actually output through Scart? I only ask as mine does have any outputs other than audio - the two scart sockets are input only.
Fourthly - check the settings on the record screen on the Archos - on the A5 you can change between Composite/component/s-video etc - so presume there will be similar options on the 604 - check you have the right input set...
Do you have a set-top box of any sort? You could try plugging into that to see if you get a picture.
On my set-up, once you cancel TV out, it goes to the screen you mention with the TV logo and then the picture comes up very quickly.
Hope this helps but, if not, I am sure there are other, more experienced ARHOCSers out there!