Hay Chelo
How about putting a test light or volt meter on the wire feeding the starter when you press the start button ?
That would determin the good or bad relay thing.
I took the decompression Senolid off mine when I put on the larger fuel tank because there wasn't room under the tank for it. Well , I found : that with a stock engine I didn't need it.
It might be better to leave it on and working since Suzuki thought it needed it ?
So , test for
electron flow Voltage at the stater with the start button pushed .