What are all the ineligible countries that do not restart the 90-day Visa Waiver into the USA?
A link on the Visa Waiver Program page (under "Trips to Canada, Mexico, or nearby Islands") points to the Closed Loop Voyages page from the CBP. According to this page, the definitions of Contiguous Territories and Adjacent Islands is:
Contiguous Territories are any country sharing a common boundary with the United States. Canada and Mexico are contiguous to the United States.
Adjacent Islands as follows: Anguilla, Antigua, Aruba, Bahamas, Barbados, Barbuda, Bermuda, Bonaire, British Virgin Islands, Cayman Islands, Cuba, Curacao, Dominica, the Dominican Republic, Grenada, Guadeloupe, Haiti, Jamaica, Marie-Galantine, Martinique, Miquelon, Montserrat, Saba, Saint Barthelemy, Saint Christopher, Saint Eustatius, Saint Kitts-Nevis, Saint Lucia, Saint Maarten, Saint Martin, Saint Pierre, Saint Vincent and Grenadines, Trinidad and Tobago, Turks and Caicos Islands, and other British, French and Netherlands territory or possessions bordering on the Caribbean Sea.
In addition to Greg's answer. Adjacent islands are defined in Immigration and Nationality Act §101
The term “adjacent islands” includes Saint Pierre, Miquelon, Cuba, the Dominican Republic, Haiti, Bermuda, the Bahamas, Barbados, Jamaica, the Windward and Leeward Islands, Trinidad, Martinique, and other British, French, and Netherlands territory or possessions in or bordering on the Caribbean Sea.