The internal pages won't be penalised because there is no content on the homepage.
The title tags are critical though as said above, without a doubt.
Also I don't care what anyone says, but there is a lot of bull**** surrounding
SEO and while it might be true, having relevant links is still pure conjecture - THAT is a fact.
All I know is that title tags and inbound links definitely help.
Things like relevant links, H1/H2etc tags, alt tags, url, relevant anchor text in the inbound links probably do help, but no one apart from google really knows how much.