Battery charged, starter button pushed - neutral and oil light dimms a bit and no audible relay click. I want to ask you fellows if that's a defective starter relay you think?
Also are these: http://www.ebay.com/itm/Starter-Relay-f ... 1e68a74e8c relays alright?

May be your starter relay.
The one on ebay only has a 15 Amp fuse and the nc30 is a 30Amp fuse. The suggested one is also square unlike the round nc30 ones.

Do you have a multimeter, if so set to volts DC and connect one probe to each of the heavy duty wires on the starter relay. Should measure 12 volts with ignition on, press starter button, voltage should drop to zero. Would also suggest you monitor battery voltage with multimeter while pressing starter button to make sure battery voltage remains above at least 10 volts when starter cranks.

Thanks magg and skinny! I'm taking it to the mechanic tomorrow (no tools), what else should I check on the electric side, how do you check for problems with earth(body)?