No way to tell for sure from what you have told us. It could be any of those... Hard drive, memory module, power adapter, DVD drive, or dirt, hair, fiber and heat.... or even a power switch
First, check carefully for any lights or noise when you depress the <ON> Button. Then gently wiggle the plug from the power adapter where it plugs into the laptop as you depress the <ON> button to see if any lights or noise happen.
You can buy a new power adapter for about $11 to $22 on eBay, but that would take ten days to arrive. Can you borrow a power adapter from anyone... anyone that fits will be good enough for a brief test.
Second, do the sniff test with the covers off, as you try to detect a burned odor.
Third, you remove one memory module and try to turn on with the other. Then change the two around and try with the other module.
Some gateways have had trouble with the power adapter, but it is not easy to test at home. A good technician can use an instrument to test the power output. The hard drive should not be dying this soon unless it has had some impact.
Fourth, you can remove the hard drive from the section on the base of the computer, you can test with another or test yours in another laptop of similar configuration.
In short, get a tech smart person to look it over for you... of have a repair shop do an analysis... which will likely cost about $40