Ask my employer for the repairs?
Ask for a new laptop (company would own it)?
Any other option?
While it might sound like a saving for the company, using a personal laptop for work is a significant risk for any intellectual property your employer wants to protect.
When I started working in a small company (less than 10 employees), at the end of the interview that got me hired the owner/CEO expressed his concern that there was not a computer for me, and was glad I proposed to use my personal laptop, as it would save him the money of buying a new one.
Then some weeks later, after hearing on the radio about industrial espionage, he rushed into the office, yelling "I want no personal laptops in this office, who did ever give you permission to use one?". I calmly answered that he had agreed to such usage, but that once I was provided with a company laptop I would have been more than happy of leaving my laptop at home.
This said, I would make clear with your employer that they are hampering their own IP by allowing unmonitored computers to access their company network. Should any of you be subject to a ransomware attack, they will learn the lesson the hard way. As such, company owned and managed computers can be safer.
Regarding your own computer, it would be worth asking for the repair to be covered by the company: things staying as they are today, you cannot perform your work with a broken system, it's again their interest to have you working.