First of all, have created your recovery disc? You better do it first.
1) Which GPU is the one crashed and did you install any new driver in the last 2 days? How's the temp? There is a new driver update released in the past week, maybe you can try to download it and update you driver.
2) Your laptop comes with 4 or 8GB RAM? BSOD can be causes by hardware (such as RAM incompatibility, HD failure) or software (driver, corrupted Windows files). There is a software out there (bluescreen viewer, or something like that), download it and check the minidump file to identify the culprit.
3) Try update your Wireless card driver. Please check you wireless card brand before you download the appropriate update. Check also your Internet connection. The problem could be originated from your ISP too.
4) Looks normal to me.
5) Please read Checksum is Invalid
  Or it could be that motherboard battery is dead. You could either replace it yourself or bring it back to the shop you bought from and launch a complaint to them to replace it for you. To replace it yourself, first get a replacement battery (CR2032 button battery) and a "-" screwdriver. Open the backplate (careful, this is one of the trickiest part) and once you've open it, you should be able to see the battery near the harddisk. Replace the battery, and close the backplate (the second trickiest part).

For 1,2 and 3, if the problem persist, you could opt to do recovery using the recovery disc you've created. If all else fail, bring it back to where you bought it from and demand a solution from them (warranty or a new unit, perhaps)

These are my opinion and you should wait for other user for their opinion on these matters.

Editted: added HP technical support website

For the above pic, notice that most of the taskbar icons are blank (missing AVG, grapics controller, etc. Even the wireless connectivity bars are missing, just an empty space between my speaker icon and the HP wireless assistant icon.)

Eh... this issue i dnt think related to Hp. It's software problem. I believe u can customize the icons setting. Why dnt u update the window or reformat ? Hv new BIOS to update ?? Some time i also facing such issue too but it's rare.

For HP Support Assistant, I think u should try reinstall the software or dnt need to use it. For me it's just wasting memory and space 

By the way, hv u using any software which will roll back ur window into previous one ? Such as  Returnil Virtual System, if do, pls un-click the function and update ur window and turn it back when everything has done.

If not mistaken RM3290 without beats headphones one~ It's hard to exchange to a new one for software problem. If it's still there, i think u can send it to HP service center at pinang, Their service good unlike Mlc service ^.^
Driver