Edit: I have Zero ether in my account so I cannot transfer remaining tokens to another account. In order to transfer I need to buy ETH. Is it a good idea to buy ETH and transfer to old account then transfer remaining tokens to a new address?
That's the very least you can do for now. It's better to transfer all the remaining crypto assets you have in your wallet before it's too late. You can buy Eth in crypto exchanges and transfer them to your MEW so you can have a gas to transfer all your cryptos in a safer wallet.