i think you don't have enough money to pay for the gym membership, try working in the restaurant or grinding in the dungeons to get the money to pay for the gym membership, if you're still unable to use the gym then i think its a glitch which needs fixing and i think you can also use the basketball room in the university after you're done with classes to gain strength.
it really depends on how many days you want it to be, if you want for a year then that will cost some money, don't remember how much but its takes a while to collect if you just started the game, i would say that work in the restaurant or kill enemies in dungeon to get the money to get the membership (sorry for the late reply)