Answer to "Why is my Chromebook getting hot and making noise?"This could happen for A number of reasons. The 2 most common are “no air flow” on the bottom when in use. Make sure when you use your Chromebook, you have good “air flow” under it, on a hard flat surface is the best. Don't keep it sitting on A pillow, mattress, blankets, ect. this blocks the air flow under the Chromebook. The 2nd reason, A bad fan. All Chromebooks don't have fans, but for the books that do, fans get full of dust, loose exc. over time. Best Buy is A good place that can replace or repair fans for cheap. Also checking the bottom of the Chromebook making sure the wholes are not full of dust is a good start.
Answer to "Is the motherboard fried?"i think your right, Needs A mother bord or has hard drive issue. I would guess mother bord.