Media Encoder takes an hour to render 4 min AE video

AE doesn't use the GPU the same way other apps like Premiere do. It does most of its rendering on the CPU, and if you're not using a lot of GPU-accelerated effects (and even if you are for certain parts of your comp) you won't see high GPU utilization across your entire render. In your original post, it sounds like multi-frame rendering wasn't being taken advantage of by AME if you were barely seeing any CPU utilization, but it definitely is enabled in After Effects if you're seeing max CPU utilization.

What do you mean in your last sentence when you say the "same file" is taken into AME and converts to H.264 in less than 2 minutes Are you talking about the rendered MOV or AVI you mentioned in the first sentence? If so, that makes sense because AME can now use the GPU to transcode as H.264, but it doesn't mean the GPU is used the same way to render your AE project in the first place. Rendering is an incredibly complex topic, especially when you're taking about performance and rendering in After Effects. Your reply still doesn't give a lot of information and it's unclear if your problem is solved because your H.264 conversion happened in less than two minutes, but you said it took over an hour in your original post.

When asking for help on these forums, you have to imagine the people responding don't know anything about your setup or project at all and you have to be very explicit; there are too many variables to consider in each situation.