[ColinTheAmpMan1]

The circuit diagram you give looks right, but my eyes see the gain controls as being 500k and 300k - they are both supposed to be 500k.
If you aren't getting any of the direct signal to the output, that is going to be because the two halves of the pre-amplifier ECC83 are dead or aren't passing any current, as sortedradio says. I would check the power-supply first; the voltages on the positive ends of the 20uF capacitors ought to be present and get lower as you go from the capacitor closest to the HT rectifier to the one feeding the 100k resistors on the ECC83 anodes - take care as the voltages ought to be around a hundred or so volts and can hurt! If there is HT present on the anodes of the ECC83 (pins 1 and 6), then the cathode circuitry, which is common to both triodes (a cheapskate technique) is likely suspect. You say that the heaters of the valves are all glowing - make sure that you can see two glowing heaters in the ECC83. I wouldn't mind betting that once you solve problem of not getting signal to the output, you will probably have a working Copicat.
One problem that can arise with these valve Copicats, while a highly desirable bit of kit, is that they can run hot and wax will melt out of the mains transformer when that happens. They also, like most tape-based echo units, suffer from noise coming from the tape-loop splice, which can be disconcerting at times.
While the unit, as you say, doesn't have a connection to mains earth, this is because the output cable will connect to the earthed chassis of the amplifier that you are running it into, thereby effectively providing an earth. This wasn't particularly good practice, either. It would have been better to properly earth the Copicat to mains and to break the ground connection of the output cable. This would have provided a proper earth and eliminated any earth-loop between the Copicat and the connected amplifier. Oh well, you could make this modification for better safety, but it would detract from the re-sale value.....
Colin.