From the sounds of it your system is overheating.
First lets get a tool installed so we can monitor the thermal sensors and what the fan is doing. I like this app Temperature Gauge which you can download from the App Store, there are others out there that are just as good.
While that is running and you are monitoring the sensors see if one is getting to hot and let us know. Lets start thinking of other things here that need to be looked at
Lets look at the HD and see how it looks often a system that is overheating can be encountering issues with the HD. Is this the original HD that came with your system or is it new? If it's a new HD please give us the model info on it.
Next we need to look at the systems memory is it what came with the system or did you upgrade it? If you did upgrade it what are the module sizes?
Have you also cleaned out old programs and files so your HD has at least 1/3 free space? If not you may want to trim the junk off and then defragment the HD. But before you do this make sure you have a good backup of your apps & data and run HD diagnostics to make sure the HD is in good shape.
Lastly, have you cleaned out the dust build up internally (the fan and the heat sink fins? If not it may make sense to do that and given the age of your system the thermal paste that helps move heat off of the CPU & GPU may need to be refreshed (this is a more advanced task).
You really need to get the temp monitoring software on your system. It also sounds like you may need a new HD, for now lets test it out.
You'll need to create a bootable CD with your copy of Mavericks, as your system doesn't have a FireWire port and I don't think Apple ever enabled boot up with USB drives on the MacBooks.
See if there is a newer EFI for your system. Follow this Apple TN EFI & SMC firmware updates for Intel-based Macs After updating you could try booting up via the USB to be sure. If it works then use it Vs the CD.
Once you get your system booted up you'll need to launch Disk Utility and then run it doing disk repair and then repair the permissions as well on the drive. If it fails you may need to reformat the disk and re-install everything. But before you do anything on your disk make sure you have a backup.