EVGA recommends a 300W or greater PSU which is a recommended overall system requirement "based on a PC configured with an Intel Core i7 3.2GHz processor" (link)..The GTX 750 SC itself is a 55W card (see details)..Use this PSU calculator to get a good idea of your specific system wattage requirement.

Ok, thanks for all your help! I used the calculator, and it said I'd need a minimum of ~290w. Do you think this psu could support the 750, at least for a little bit?
 

 
I do plan on buying a new power supply in the near future, when I pick up a secondary HDD.
 
EDIT: I just noticed this review on Amazon, what do you think?
 

Geforce132
Ok, thanks for all your help! I used the calculator, and it said I'd need a minimum of ~290w. Do you think this psu could support the 750, at least for a little bit?
 

 
I do plan on buying a new power supply in the near future, when I pick up a secondary HDD.
 
EDIT: I just noticed this review on Amazon, what do you think?
 

That seems to be a incompatibility with the motherboard bios (HP, Acer, Dell, Ect. pre-built pc's are notorious for that), not a power issue. 

Thanks for all your replies!
 
It turns out that a 750/750 Ti won't actually fit on my motherboard. It's just slightly too large for my (old) motherboard to handle.
 
Here's two photos:
 

 

(Yes, I know I need to clean my case.)
 
That little black component sticking out might be able to go inside the gap between the plastic case, and the board itself. What do you think?
 
(this gap here):

tucker147
It might fit.
 
Also, what motherboard is that? put the model number.
If it's from a HP, Dell, Acer, Ect. the 750 may not even work at all.

Yes, please post the model number of the system and/or the motherboard. 

Yeah, it's most likely not going to work with that motherboard (acer's boards are a PITA(only fix that I know of is to buy a new mobo unfortunately).
 
Just out of curiosity, what cpu are you using?

I'm not sure what that black piece is, but it doesn't look like an electronic component to me, if that's the only issue that's keeping you from upgrading your card.... could that little piece possibly be snipped off without harming anything?
 
If not, I wouldn't recommend a 630, the performance would be horrible, I'd recommend a GTX 650 class card atleast...... a 740 might suit you, it has 650 class performance, and a much smaller cooler than any of the 750 TI cards
EVGAs GT 740 SC singleslot card might be just what you need
Don't waste your money on a 630 though, if we're talking about performance per dollar then it is an extremely overpriced card!
 
Edit: Hmmm, just noticed the singleslot versions of the 740 use DDR3 instead of GDDR5, the other versions have GDDR5 but have larger coolers which might not work in your system. :/