Computer doesn't turn on correctly

Did you install the 700W PSU and graphics card into your Inspiron 660 or is this a factory upgrade?

I'm not sure, but i think Dell does not use a standard ATX PSU, i think they changed the pinout on the connector so a standard PSU will not work on a Dell system. If you did install an ATX PSU into your 660, you'd be lucky if you have not blow up the mobo, if i'm correct about Dell PSU's not being standard ATX...

If you have a dell PSU, then either the Dell PSU is faulty or the Dell graphics card is faulty.

I installed it myself

OK.

Unfortunately Dell is not at all clear within either their Owners manual or the Reference Guide (both available here) what standard their PSU actually complies with. Dells PSU may or may not conform to any recongised industry standard (like ATX, TFX, etc) so installing a non Dell PSU is fraught with difficulties.

This means it may not be correct to just buy a non Dell PSU that fits and simply plug it in. Mechanical issues are obvious easy for most to spot as it wont fit within the case or plug into the main connector (with a light touch). BUT there may be electrical and logical differences between the Dell PSU and the non Dell PSU you bought that are not obvious. 

So the questions you should look at anwering are:

- who made the PSU and what is the model number?
- does the PSU manufacturer certify that their PSU can be used in a Dell Inspiron 660?
- can Dell support state whether their PSU is proprietary or standard ATX?
 (but good luck in truing to get a real tech answer out of support)
- does your system work reliably if you remove the graphics card and install the old Dell PSU?
 (you now know your system is OK and not damaged)
- does your system work reliably if you now install the new PSU but not the graphics card?
 (you now know your system and new PSU is OK and likely the GPU is faulty)

If your system does not work (or work reliably) with just the new PSU installed, it may be the new PSU is faulty or simply does not conform to Dells design!

Note that I've read on some posts that the PSU in the non slim Inspiron 660 uses an ATX compliant PSU but such information is not documented in any official Dell docs!

You should be able to manually check some aspects of the PSU if you have electronics skills and know about electrical safety and how to safely force a PSU to power up outside the computer. If 'yes', then it's a matter of comparing the voltages at each pin between the Dell and non Dell PSU to ensure they are indeed compatible. But note that if Dell does not use the ATX 'power good' signal or 'PS on' signal as defined by the ATX standard, even though all voltages on the pins themselves are the same (between the Dell and ATX designs), there may be some other logic that needs to be handled during switch on which may or may be handled correctly with the non Dell standard ATX PSU.

If all the above talk of 'voltage' and 'power good' and 'logic' confuses you, then it's not a good idea to be messing with getting an ATX PSU working in a system that potentially uses a non ATX PSU... Be warned that people have been killed by messing with faulty computer PSU's as there are lethal voltages within. So unless yoy are skilled, get someone that knows what they are doing to check your hardware and don't play with things (that may kill you) that you don't understand.

But if the 660 really does take a standard ATX PSU, then in all likleyhood, it's either the PSU is faulty or the graphics card is faulty (assuming your other hardware is indeed all OK). So answering the above questions yourself will go a long way to resolving your problems.

I've been using a Seasonic SS-660XP2 ATX power supply in my Dell Inspiron 660 for about 18 months without any problems.

SS-660XP2 ATX POWER SUPPLIES are Not supported by Dell.

Dell power supplies are EPS12V PFC 80% Bronze.

http://www.smps.us/EPS12V_Spec2_92.pdf

The Seasonic SS-660XP2 is ATX12V / EPS12V 80 Plus Platinum Active PFC F3.

To troubleshoot the problem, I’d remove the new video card. If the problem persists, the new power supply is probably bad. Reinstall the old supply to confirm.

The exact PSU i am using  is a Thermaltake TR2 700w, and the GPU im using is a EVGA Geforce GTX 460, if that helps

https://www.google.bg/search?q=dell+atx+psu+pinout&safe=off&client=firefox-a&hs=qtM&rls=org.mozilla:en-US:official&channel=rcs&tbm=isch&tbo=u&source=univ&sa=X&ei=n9sCVLCNB8SaygPyiIKgCA&ved=0CB0QsAQ&biw=800&bih=461