laptop keeps freezing up/crashing

i bought my HP G62-340us laptop new just under two years ago.

This computer worked relatively okay for awhile although on rare occasions, it would freeze/crash on me, leaving me with just a dark screen and nothing i did would unfreeze it, excepting performing a total shutdown via the power button and a restart.

Now the computer is freezing several times a day, leaving me with either a dark screen, a white screen, a blue screen [rare], and sometimes, a white screen with black horizontal lines spaced about a centimeter apart; again, all i can do is a hard shutdown via the power button. On several occasions, when i have tried to restart the computer, it would not boot up at all, causing me to again do a hard shut down, and try again. i have even inserted a system repair disk to try to restart it. i have run all the diagnostic tools i have found on this laptop, but nothing has alleviated the sudden freeze up. [it sometimes happens when i am not even touching it!] Indeed, the diagnostic tools shows my laptop is working properly with no issues.

i have not been hard on this laptop. i do not play any games on it, and only have used one of the USB ports to save files. i only use it to check my e-mails, search the web, and use a word processing program. i rarely ever take it anywhere - it mostly sits on my table and therefore doesn't get shaken up [nor bumped] at all; i am extremely careful whenever i do handle it. i still have most of the original storage on this laptop as i mostly have the programs it came with and a few others i have added, such as Mozilla, Skype, Chrome, and a few others.

i suspect that the fan might not be working properly, that the laptop is overheating, and as a result, freezing up. This is only a suspicion on my part; can this possibly be the problem?

i would appreciate any help that someone can provide me. [Additional information: my DVD player is also not working properly in that it wouldn't read some DVD discs.]