OK, you have an inline fuel filter between the fuel pump and carb- OEM part# 35-816296A3, available here or at any Merc dealer.
Make sure all electrical connections are clean and tight, especially the ground to the engine block from the battery. Take the connections apart and clean them with a scraper or some emery cloth or scotch-brite. Make sure your kill switch isn't activated. First, check the 20 amp blade fuse- it's located in an enclosed fuse holder, close to the solenoid. If the fuse is OK, use a voltmeter, and test for voltage at the small red (or red/yellow) wire on the solenoid when pushing the start button. If you have no voltage, you have a faulty start button or wire. If you have voltage, next test for voltage from the solenoid to the starter,The big red wire. If you have no voltage, you have a faulty solenoid, if you have voltage you likely have a faulty starter motor.