How is the Dell Inspiron 530 obsolete?

You tell them it's slow even for basic tasks like looking at the web. If they still deny you of that right, sounds like they are wealthy but not smart at all. Unplug the CPU cable in the computer, then you may get the persuasion factor.

I’ve seen messages on the internet like this in the past (convince my parents to get me a new computer, phone, ipod, etc) , and they all seem to be missing the same thing – they all presume that the people they’re asking no better than the questioner even though not having the information unique to the questioner’s circumstances.
Is the 530 obsolete? At worst it may be unsuited to your needs….which you mention nothing about. For my needs it’s hardly obsolete. I’ve had the 530 for nearly 7 years. It’s now beginning to die on me – won’t boot to windows. I previously had a similar problem with it earlier this year but solved it by re-seating the RAM chips. Until that happened, I had to make do with a Celeron desktop – with every key punch or mouse click taking forever to register. Getting the Inspiron working again felt like getting out of school the day before vacation, it was that smooth and responsive. I’m not a real gamer or video editor, and the 530 ran perfectly fine for me – therefore I can’t call it obsolete.
Unless you can explain what you need the new system for, no argument is going to overcome your parents’ argument. Unless you’re willing to pay for it yourself, then laggy computers are just what you have to put up with – like having a car that isn’t a hot sports car or flying coach instead of business, or staying at Best Western instead of The Four Seasons. Your parents aren’t going to go past “good enough” unless the “laggy” goes against a function you actually need – and that excludes gaming

I did give it a few upgrades myself, such as a new HDD, a GPU, processor, and PSU. But it is still slow as hell and doesn't give me a good time whenever a try to use it.

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Use it for what? For anything?
I looked over your upgrades, and I’m puzzled over some of them. The 530 can take up to 8GB of RAM, and mine shipped with 6GB; If you’re running a 64 bit OS, there’s little reason not to max out the RAM, so why did you keep it at 4GB?
Also, why did you replace your CPU when you didn’t know what it was? (you could have seen that in Control Panel). I’m personally dubious that CPU upgrades are of any noticeable value given how architecture and voltage restrictions limit you to a choice of alternatives which won’t radically outstrip what you’re already packing. Even so, an upgrade requires that you know what you’re being dissatisfied with.

250 GB HDD -> JUST ADDED ANOTHER 500 GB HDD, NOW GOT 750 GB TOTAL

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What’s your current unused capacity on each drive? Over-stuffed hard drives – even when apparently showing free space – can be a significant source of lag.