Just a note: Bridgeman is ALWAYS right. However, if you are in Chicago, they will not bother you until Spring anyway ... Call this "risk management" ebcause they have now notified you and transferred liability to you instead of them.
I would ignore the notice unless they come back at you. Offer to temporarily patch with self-leveling cement which you CAN handle. Just bury 1x4 wood on edge along the sides at the level you want to achieve. Mix and pour the cement in the morning. By evening, it will be hard enough to survive the night.
In the Spring, demolish the walk entirely and replace it properly. Frankly, this is a job for a local handyman from Craigslist. Demolition, hauling, new cement and finishing. Piece of cake.
Focus on the house!