Large files in after effects

Thie file sizes likely have nothing to do with your rendering issues. It's more likely that your Collect Files messed with the caches and they are now somehow blocking the render. Ergo, flush the disk caches first and see if it makes a difference. otherwise you may see hardware acceleration issues, but without any info on your actual project by ways of at least a screenshot of the main comp and the project window, possibly more such as the flowchart and exact system info nobody can tell you which knobs and levers to tweak to make it work and improve performance.

Mylenium

You could try lowering the pixels per inch of the PSD, you could try 72ppi. Remember to make a copy of your original PSD file before adjusting it.

We can't find the bottleneck or help you solve the rendering problem without seeing an expanded flowchart and layers showing the modified properties of your layers. We need details.

Let me be clear: image file resolution is the number of pixels. It is never the PPI. If any of the PSD layers are at 100% scale or are closer than the Zoom value to the camera at any time in your project, you cannot reduce the image file's resolution without losing quality.

If you can safely reduce the resolution of the Photoshop file,  the easiest way to keep all animations intact would be to select each layer in the Project Panel and create a proxy. I don't know of any automated way of doing that for a Photoshop file imported as a composition. The proxy will scale the proxy files to the same size as the originals without fouling up anything. You can render with proxies, and it will be faster.

Any machine that meets the minimum system requirements should be able to handle a 4K PSD file without hanging up. Render times of 2 minutes a frame are not unheard of with complex projects. I start redesigning the comp when render times approach a  minute or two a frame. The slowdown is often caused by the effects I have added, and a few tweaks will speed up the render without compromising the shot.

Is there any way you can break up the comp into individual shots? I rarely have a comp that is longer than a single shot. I do the editing in Premiere Pro or Divinci. Most of my comps are under 7 seconds because most shots in my finished movies are under 7 seconds. 

With a few more project details, we may be able to help you figure out a solution that only takes a few clicks.