I hope that there is already a papertrail showing that this person has been underperforming for a year and a half of employment, but, yeah, you're overdue in speaking with the manager about it.

Who writes his performance reviews? What are they based on? If he's been there for a year and a half and no one's flagged him, then you're limited in what you can do.

If you don't want to cause waves, just slowly limit the assignments you give him. I've been on teams where there's been dead wood and unless there's someone there to defend him (the hiring manager perhaps?) he may eventually be caught in a layoff.

The other employees should not know how much this new person is earning.

You've had this person on the team for 18 months? Have you told the line manager about the issues with this engineer? Have you documented his lack of skills in the employee file? Has the engineer had a performance review?
The "wrong" major of the other manager is not an issue here. Your failure to escalate and address the problem in a timely manner is.

So long as you can show, with documentation, why it isn’t working and how you’ve tried to remediate it but been unsuccessful, yes.

Details are that I am responsible for assigning tasks to all the engineers in my group. There is one engineer who came to us from a hiring manager as very good and was given quite a healthy salary. I mention salary because it is demoralizing the group of engineers who make less and are far more capable. The issue is this hiring manager is an English major and knew nothing about this engineer's actual skills. Turns out I can't even assign the most simple of tasks to this person, even after 18 months on the program. This engineer requires constant help from my few senior developers which wastes time. I've even tried basic training which doesn't sink in. I'm also in an awkward position as not being a manager.

Is it OK for me to tell the person's manager that I can no longer assign tasks to them as they provide no useful work and also go to the program manager and tell them the same? Managers in my company manage around 30 to 40 engineers so they largely don't know what is going on and rely on the team leads. I also worry this may come back to me as my own failure to not set this engineer up for success.