First off 700 buck will not buy you a new mac, a new mac computer starts off at 900 dollars. Second you computer is not even old, most people get new laptops at fours years, not a year and half. Third, your parents are wrong you can buy more hard drive space for the laptop cheaper then buying a new laptop.
And finally if your computer is running slow it's due to ram, 2GB is not bad, but if your using big time video editing software your looking at needing at least 4GB that will allow the computer to running smoothly and allow you to play your videos. Now this is minded that you laptop can be upgraded to 4gb of total memory.
And I'm very sure you can get a bigger hard drive and 2GB of ram for your computer for less then 700 dollars.
The 2GB of ram depending on what type of your laptop needs here is the price range that it should be in. $44-$124 seems to be the highest I'm finding the memory being in. I'm not femiliar with apple hardware, so your going to need to look into what ram your computer needs
Most new hard drive for laptops start at $170 and go down from there.
So your likely looking at spending no more then $250, maybe less. Unless of course you have the comptuer store guys set it up all for you and then there will be an extra fee included.
Otherwise just get more ram and an external hard drive, those things always go on sale.