Intel core i5 processor 2.85 GHz
4GB RAM
NVIDIA 1GB graphics card
1.5 terabyte HDD space
24'' HP screen

And a lot of awesome shit for 1000 dollars.
Is it overpriced or something ?

Or should I buy a SONY laptop with i7 and 4GB ram for 800 dollars ?

Tell us what the model number on that NVIDIA card is and we can tell you whether it's going to be worth buying.
Other than that, that seems fairly good for a $1000 laptop.
(As a side note this is what I hate about retailers. They always toss around "NVIDIA card 1gb RAM!!!" but never tell you what model it is. For all you know you could be getting e.g. a GT 120m)

Also further specs on that SONY laptop would be nice, including:
Processor power (gHz, number of cores), graphics card (brand, model number, RAM), HDD space, etc.
If it's a SONY vaio laptop i'd advise you to stay the hell away from them since they have terrible graphics cards.

What do you want to use the computer for?
Do you need mobility?
What is the most intensive thing you do? (probably gaming for you I guess)
+ everything 4zb41 said!

Also, tell us your exact name of the processor, there are at least 5-6 Intel i5 processors with different perfomance, none of them bad though, but i5-2500k is definetly for gaming, and for overclockers.

And, what kind of things are "lots of awesome shit"?

+Those above me.

I forgot the about the lots of awesome shit part
But as for the things you asked about, I wrote what was written on the specs sheet. (at least everything I remember)
Anyway, I want it for gaming and video making.

Nvidia?? GeForce 520/540 are the best ones for this price at moment.

To play games Toshiba/Asus...

I bought my pc last week:

i7 2Gz, 4gb Ram, Nvidia GeForce 540 (2gb) only 700 Euros (bonus: xbox 360 4gb)

Finding out the model number of that Nvidia 1gb graphics card is very important.
If the laptop is in a store, go into control panel > device manager > display adapters and note down what it is. Otherwise ask whoever is selling it.

Assuming the first computer you listed in your OP is actually a desktop computer and not a laptop, you could always go out and buy a superior graphics card. Something in the higher end of the Nvidia GT 500 series.

Oh yeah forgot to mention that it was a desktop computer :V
Also I'd like to ask a question, are the graphics cards important ONLY because they run the full graphics awesomeness, or something else ?

Well, if the card isn't good enough, it plain won't run recent games. Considering it's got 1gb of RAM on it, it's probably fairly decent but you never know.
No point buying it if it won't be able to play your favourite games at a decent speed, even on LOW settings.

If my computer already runs the game in high settings but with low FPS, does attaching a graphics card makes it run the game in better speed ?