First and foremost, unblock the drainage. I am guessing that your neighbor has his own good reason to actually block your drainage. I suspect that your water drainage is going onto his property and that is perhaps why he blocked the water that is draining from your property onto his?
You may have to devise a way to properly drain the water from your property without it seeping to the neighboring property. Talk to your neighbor and let him know that you are unblocking the drain to mitigate water damage to your house until you can figure a way to redirect the storm water. Approach your neighbor with reason and a cool head. The last thing you want is a feud. I know all too well how nasty neighbors can be because I am cursed with being a bad neighbor magnet.
On one cold winter day, I am standing at my kitchen sink window and I see this eerie fog outside over what looked like my lawn bubbling up. I go out there and am faced with this familiar smell. It is Tide laundry detergent. I get closer and see that my neighbor installed a clothes washer but did not hook it up to their septic system. Instead, there was a flex pipe coming out of the side of their house that reached the row of bushes where a 4' pvc pipe with drill holes was buried in a shallow grave in my yard. They were disposing their dirty wash water into my yard. How low class can one get? I simply lifted the pvc pipe and heaved it over the bushes. Then, I went over there and moved the flex pipe to face their door, anchored by a rock. I bet they got a surprise when they did their next load of laundry!!! I figured they were so ignorant that they were not worth speaking to, so I allowed my actions to speak louder than words!!!
Please do not misunderstand, I'm not implying that you are ignorant. But one must think about how their actions effect other people.