Siri activates when you press the side or Home button, but doesn't activate when you say "Hey Siri,"

Firstly, you should ensure that, under Settings > Siri and Search, the option for 'Listen for "Hey Siri"' is checked. If it is unchecked and you check it, then it will open a series of vocal instructions, i.e. phrases for you to say. Ideally, you should do this in a quiet place where another's voice would not interfere. Let me know if this works, and if it doesn't, I can look further into it.