Ancano may remain invulnerable after you close the Eye. If you have the Eye closed and cannot hurt him, you may need to reload an earlier save.
Also:
You may get to the Hall of Elements only to have Tolfdir run in and bypass the cutscene, making the staff useless. If this happens, you cannot harm Ancano in any way.
This may be a scripting error caused by obtaining 2 staves from the quest before. Tolfdir may also fail to follow you into the Hall of Elements, which prevents the completion of the cutscene and the start of the fight.
If this happens go through one of the side doors near the entrance, then come back in. Should that fail to help, fast travel elsewhere and return to Winterhold.
You may have to use the staff to gain access to the college again.
To prevent Tolfdir from running into the hall and engaging Ancano prematurely, enter the hall.Make sure to make a save, ideally at the barrier before using the Eye to dissipate it.
Stop at the door, move forward just enough to open the inner door and trigger Ancanos dialogue.
Do NOT enter the hall, move back and stay at the doorway(to skyrim). Tolfdir should move up, say his dialogue, and trigger the fight with Ancano normally. Y
ou will know it is working if Tolfdir and any follower you have with you-are paralyzed by Ancano.
At this point-move forward, use the Staff on the Eye and kill Ancano.
The key is NOT to move forward with Tolfdir, but remain at the doorway, this should, hopefully, resolve the invincible Ancano problem without resort to elaborate workarounds.