First off, YES, it's possible. A HELOC, Home Equity Line of Credit, is essentially a credit card attached to your house. Your parents can borrow against the equity in their home and use it pretty much however they want, including investing in your projects. They just need to be careful that they can make the payments on it or the bank could foreclose.
Secondly, they sure CAN invest in your projects. Now, whether it's a good idea or not is something else entirely. You'd better be sure you're going to be able to return their investment plus interest, or Thanksgiving dinner could get real uncomfortable.
As far as the LLC, that's no problem either. They can make a personal loan to the LLC, or they could become members of the LLC and invest that way. Either way, make sure you've got a rock solid operating agreement in place that lays out exactly what happens if the investment goes south.
Just remember, we're talking about your folks' home here. If you screw this up, it's not just a failed business venture, it could put their house at risk. So do your due diligence. Get advice from professionals. And above all, make sure it's a deal that makes sense.
Keep grinding, keep learning, and don't be afraid to take calculated risks. That's how you win in this game. Good luck.