What is the worst an attacker could do with full control over the blockchain?
You're correct that a miner with 100% control could not forge transactions, the nodes would just ignore them. They could perform a '51% attack' though, trading coins for another asset (confirmed in 'block x'), and then going back to re-mine a new 'block x' that does not include their transaction (so now they control the asset they traded for, and have their coins back. The network could catch on to this, but nothing 'invalid' will have happened). 

A miner can censor transactions though, so they could just mine empty blocks endlessly, effectively stalling out the network. 

Perhaps more profitably, they could set a very high minimum fee for a tx to be mined, essentially using their monopoly to extort users for higher fees. This could be done covertly so as not to raise suspicion: the miner could generate their own high-fee transactions to fill up a portion of the block, forcing other users to pay higher, or be excluded. The miner would receive 100% of their fees back since they control 100% of the hash power, but it would be tough to tell this is happening from the outside.