I've read alot of post about the HP G62-340US Freezing, Blue Screening, Fans Racing, Turning Off repeatedly, Slowing down basically to a halt and Hard Drive Problems.
The Hard Drive issues are a different problem, probably HP trying to save a dollar and buying cheap factory seconds.
But what I've found worked for me in solving all the other issues mentioned, was shimming the processors, both the AMD CPU and the GPU. I noticed that the fan would race, but was blowing cool air, which is a sure sign that the heatsink is not contacting the processors, thus not relieving Any of the heat which causes all of these symtoms. Like the older HP DV Series that HP got sued for, I found that there is a gap between the heat sink and processors, which after totally disassembling the laptop to get to it, is easy to see (on mine anyway), so once copper shims were installed to fill that gap and proper thermal paste was applied to transfer the heat outside the laptop as it is suppose to do, all the above issues were solved, well for the last 11 months so far anyway. The Hard Drive in mine was basically junk from purchase, but I replaced it with an old ssd drive that I pulled from another machine, and again is still working fine.
Long story short, In my opinion, HP is just a extremely poor quality machine, cheaply made, and for the most part you are on your own, cause "HP Tech Support" just seems to be reading some cookie cutter response that they have written before them when you call, and are merely guessing at the problems you are having. I learned the hard way, to not expect a logical response, cure, or offer to correct the problems. They (HP) didnt listen when the DV Series was faulty (Until they were sued) and likewise dont listen now. The best cure is to NOT buy HP.