Will my PSU run this card?

What is the rest of your system? Your PSU can push 25a on the +12v for 300w total. the 650ti uses about 150 at peak, but the rail is also shared with the processor & motherboard.

Also, logisys is a crappy PSU. Not only are they unreliable, but that unit in particular is very poorly designed. 30a and 55a on the 3.3v and 5v is a waste, while 25a on the 12v is very weak for a 600w PSU. Also some PSU manufacturers (i'd wager logisys among them) list peak wattage on the sticker instead of RMS. Peak wattage is what the PSU can tolerate in spikes only, not as a continuous wattage.
 

AzureNinja99

Honorable
Aug 5, 2013
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0
10,540

Here are the other compoments http://i.imgur.com/8bAWOuo.png
 

AzureNinja99

Honorable
Aug 5, 2013
28
0
10,540


Thank you! If I don't upgrade my PSU, what problems might arise?
 
If it is as I suspect, and Logisys is listing peak output on that sticker, then your system will be consistently running over the PSU's RMS. Your PSU will fail at some point, taking out any number of other system component when it does. That's assuming it doesn't fail simply from the cheap components and construction.

A failing PSU is capable of destroying everything in your system.