First of, there's no such thing as a memory battery. There is, however, a CMOS battery which could be described as a memory battery. It keeps power to the CMOS which is what keeps the saved changes to the BIOS. This, however, is not your problem.
A few questions.
1. When trying to boot does it just flash with a blue screen and reboot? This is called a Blue Screen of Death, or BSOD. The act off rebooting over and over is called a Boot Loop. This can be caused by a damaged OS, or a bad hard drive. If this is the case then the best thing to do is reformat. This can be done by inserting the OS disk and following the instructions to do a "Factory default, or factory settings" restore. This will erase everything on the hard drive and reinstall the OS like it was new. If this does not fix the issue, or fails while attempting, then you probably have a bad hard drive.
2. Does it randomly BSOD while running something and reboot? If this is the case then there could be a driver error. Run all updates for your OS, even the non-important ones and test the waters. This also may end in reformatting.
3. Does it randomly restart without any errors at all? This could be a power or overheating issue. This hardware related issue is not something that could be fixed by you and probably needs to be sent into a professional tech.
On a final note. PLEASE PLEASE PLEASE do not open your laptop. Even with a minor understand of what is in there you can still seriously damage it. Laptops are not as simple as desktops to take apart and put together again.
Edit for you update:
The are a few different types of noises.
1. Clicking. This comes from the head of of the hard drive clicking inside the case. If it is a constant click, and if you still boot into windows, then plug the hard drive into another machine/external into this one and get the data off pronto. If it doesn't boot to the OS then you can ship the hard drive off to a clean room facility, something like Drive Savers. They are expensive but should be able to get the data.
2. Loud grinding. This is usually due to the hard drive dying. If this is the case then you should follow the procedures in 1 to get you data off.
3. Loud spinning. Could also sound like a big fan. This is probably your fan dying. It's overtaxing itself trying to keep up and just failing at it. This could explain your above average heat issue.
4. Loud humming. Probably a dead fan trying to spin but not quite making it. Would explain your above average heat issue.
5. There could also be a lot of crap in your heat sink causing your fan to spin a bit faster but overall not helping much because there's not sink-air contact and convection cannot take place.
Sometimes when things go wrong and one is asked if there is a noise, people will hear the normal noises of a machine and think them odd. Not saying you are doing this now, but it is something to think about.
If you find that the noise is coming from the fan then you should get some canned air and blow it out through the vents next to it.
If the air doesn't help, then the best idea would be to take it to/send it into a professional. Most hardware issues cannot be fixed.