The relay clicking is usually a promising sign
Next check ...
- after power on (and even if you have no screen display) press Enter a few times and then type CLOAD and press Enter.
The relay should click as the computer tries to start the cassette and search for a file.
You will have to press reset or switch off afterwards as it will carry on searching for a cassette file.
If that works, then the computer has at least initialised, even though you may not see a display.
Another check ...
- after power on again, press enter a couple of times and type PLAY "CDEF" and press Enter
You should hear 4 notes of a scale, which proves that the system is working (assuming that your TV/Monitor connection has sound).
If it passes that test, then you are into video issues. Which are you using - a TV (on the RF output) - or a display connected to the Monitor output?
Perhaps it would be best to continue this conversation in the Dragon Hardware section with a brief update of your findings....