I finally found the source of the problem. It was in the Firefox settings that deals with the items that are cleared when Firefox closes.
- Browsing & download history
- Cookies and site data (12.4 MB)
- Temporary cached files and pages (257 MB)
- Saved form info
- Site settings

By default the first 4 items have always been checked as far as I know. When I unchecked "Cookies and site data", things speed up with the exception of Gmail. The initial window loads fine, but then it is still painfully slow loading the rest of the data. It flashes between "Transferring data from mail.google.com" and "Transferring data from apis.google.com". It appears to be repeatedly trying to download certain data that it cannot get access to, and I don't have a clue what the problem is. If I wait long enough it eventually finishes loading.

J.A. Coutts