Well you don't need to buy off ebay, also tell them this, when you do buy custom, you can pick from a few manufacturers that offer lifetime warranties. Only for the video card and ram though, but those are parts that most often go bad. You get a lot more for your money, and you can upgrade it bit by bit whenever you want without the worries of incompatibility.
I've been building computers for ages, tell your parents to take a look at this response if they can.
With custom computers, you get more for your money, and higher quality parts. Brand names always use the cheaper parts possible to keep costs low. Why do you think most people have issues with a brand name dying within 1-3 years? Meanwhile, all the computers I've built are still alive, I have a 8 year old, 6 year old, and 3 year old rig all next to me up and running.
Custom pc's = longer life span due to quality (if you buy the right parts, and we can recommend all the right ones), upgrade ability so you can make a computer last by just upgrading a few parts here and there, no need to buy a whole new computer, you can just reuse what you have and change out others to make your computer stay up to date.
Overall, you get more for your money out of custom pc's. Show your parents this thread and hopefully they'll change their mind, cause for what your getting for that 500 dollar rig, is unfortunate. In most scenarios, very low budget brand names computers are ok as long as you need a monitor/keyboard/mouse, but if you already have those, and are getting only the tower, it's better to go custom. For middle/high range, it's ridiculous to go brand name, you overpay for the parts, when you can get a much more superior computer that will last longer for lower cost.