Just like the title says, is it possible to block crypto currencies if the government decides to?
They could enforce the ISP to block online payments made or something like that, is it possible?
Not really doable.
cryptocurrencies are designed to counter this sort of government intervention in transactions. There is no central point of failure, for a country's government to say no to bitcoin completely they would have to shut down every single node that runs bitcoin which is impossible. This is in stark contrast with centralized payment processors such as LibertyReserve and e-gold which all got taken down very easily.
Your idea about ISP blocking online payments will firstly spark public outrage and secondly, probably wouldn't work very effectively as workarounds can be implemented quite easily. And plus, how are they going to block bitcoin transactions in the first place? I'm not aware of any obvious ways of doing that.