Verbs

I was reading the long, drawn out explanations of verbs in the Parrott book. It made me reconsider my original simple definition of a verb: an action word. But that definition does not give a verb justice. There are many types of verbs and many forms and many uses. It is not fair to say that verbs exist in a sentence in order to express action. I like the quote written in Anderson's book,

"The verb is the heartthrob of the sentence. Without a verb, a group of words can never hope to be anything more than a fragment, a hopelessly incomplete sentence, a eunuch or dummy of a grammatical expression."

In reference to modal verbs, I was trying to make a comparison of modal verbs in English with those of Spanish and Italian. In the Latin-based languages I mentioned would the modal verbs be "dober / dovere" (to have to)"poder / potere" (to be able to) and "querer / volere" (to want to)?