The custom Javascript or other CSS setting for the page or template may be causing other parts to malfunction. To test whether this is the case:
  1. Create a new Layout based on the system default stylesheet and place one content placeholder on the layout.
  2. Create a new Template based on the Layout from Step (1).
  3. Create a new Page based on the Template from Step (2).
  4. Place the same part(s) that are malfunctioning onto the Page from Step (3).
If this page allows the part(s) in question to display without malfunctioning, then the design of the original Page or Template is causing the problem. Remove the Javascript or CSS that is causing the conflict.