Could BitCoin network be destroyed if blockchain would get corrupted? This thought came to me whilst watching mr. Robot where the entire database of a financial corporation has been encrypted. 

Would that (in theory) be possible if a virus was spread that would target machines in BitCoin network and encrypt the blockchain stored on these machines? 

After that attackers would demand users to pay them in a new cryptocurrency which is not available for purchase yet. This would force all the users to mine their currency and (in theory) this currency would become equally as valuable as BTC since the cost would be the entire blockchain.
The answer would likely be no.

Since blockchain is anyone that has fully synced so it would take the attacker for a long time to destroy every single one of the blockchain. Bitcoin node also can reject an bad data (and temporary ban them) so that it does not mess up the blockchain.

Even if attacker managed to attack it, bitcoin core developer would likely to update their bitcoin core for a higher security before attacker can even finish attack all the blockchains.