Some things to check. Have permissions changed during your migration? Sometimes those things change unexpectedly. Use Chrome inspector to see if any Javascript is failing to load (look for the red x).
Have you updated permalinks?
Is your new dedicated environment able to support the requirements of everything you’re running?
If your code hasn’t changed, but only your hosting environment, you’ll want to look there first. Do you have access to error logs? Look for resources failing to load.