A participle must be in a verb string in order to behave as a verb. Without an auxiliary, a participle plays a non-verb role in its sentence.
Arriving home late, Priscilla rushed into the kitchen.
She was thinking about the burnt potatoes.
Remember that participles are parts of verb strings. They need auxiliaries to do a verb's work. If a participle has no auxiliary in front of it, look elsewhere for the sentence's verb.
When the word to stands in front of the base form of a verb, it creates an infinitive. An infinitive plays a non-verb role in its sentence.
To know him is to love him.
I want to bring him with me at Christmas.
The infinitive serves as the name of a verb. It can play several roles in a sentence. However, if a base form has the word to in front of it, look elsewhere for the sentence's verb.
Tip for distinguishing non-verb forms from verb forms: A verb form ending in -ing can act as part of a verb only if it is in a verb string (preceded by an auxiliary). A base form with to in front never plays the role of verb.
Chapter 5 explains the behavior of these non-verb forms in more detail.