This is a basic question, but I cant seem to find anything that would prevent it, but can you play the Inflict spell AND a weapon during a combat check?
Nope. Hawkmoon will probably be along with the copy/pasted rules bolded in the perfect way for maximum understanding, but the shorthand is essentially "you can only play one card that defines your check." So Inflict and a weapon say, "For your combat check..." And that tells you what you're rolling, what skills you're using (Strength or Melee Skill + 1d6 for a Quarterstaff, Wisdom or Divine + 1d6 for Inflict). You can then play additional cards that augment that check (bury your Grizzled Mercenary for an additional 1d8, play a blessing for an additional die), but you can't play multiple things that determine your initial action.
Determine Which Skill You're Using... Some cards allow you to use a particular skill for a specific type of check, or to use one skill instead of another. (These cards generally say things like “For your combat check, use your Strength or Melee skill,” or “Use your Strength skill instead of your Diplomacy skill.”) You may play only 1 such card or use only 1 such power to determine which skill you’re using.
As Dave said, it isn't that the spell is an Attack spell, but that they both say "For your combat check..." which means they are the kind of card that determines the skill you are going to use for your combat check. And you can only play 1 of them. There are some attack spells that don't say "For your combat check..." but instead affect a combat check. You could play a weapon and a spell like that on the same check.