From what I can find, here is a list of processors that are compatible with your motherboard:
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Lynnfield Intel® Core™ i7-880 Processor
Lynnfield Intel® Core™ i7-875K Processor
Lynnfield Intel® Core™ i7-870S Processor
Lynnfield Intel® Core™ i7-870 Processor
Lynnfield Intel® Core™ i7-860S Processor
Lynnfield Intel® Core™ i7-860 Processor
Lynnfield Intel® Core™ i5-760 Processor
Lynnfield Intel® Core™ i5-750S Processor
Lynnfield Intel® Core™ i5-750 Processor
Clarkdale Intel® Core™ i5-680 Processor
Clarkdale Intel® Core™ i5-670 Processor
Clarkdale Intel® Core™ i5-661 Processor
Clarkdale Intel® Core™ i5-660 Processor
Clarkdale Intel® Core™ i5-655K Processor
Clarkdale Intel® Core™ i5-650 Processor
Clarkdale Intel® Core™ i5-650 Processor
Clarkdale Intel® Core™ i3-560 Processor
Clarkdale Intel® Core™ i3-550 Processor
Clarkdale Intel® Core™ i3-540 Processor
Clarkdale Intel® Core™ i3-530 Processor
Clarkdale Intel® Pentium® Processor G6960
Clarkdale Intel® Pentium® Processor G6951
Clarkdale Intel® Pentium® Processor G6950
If you upgrade your power supply to the Corsair unit you listed, you'd be able to successfully upgrade the processor and add a graphics card like the GTX 750/750Ti. I wouldn't recommend going with any graphics card more powerful than that as it would not perform to it's abilities; being limited by even your upgraded processor.
Now these processors are not readily available and you'll likely need to find a used one, and with that comes the risk of a used processor that's been abused and/or faulty. That's the risk you take with used components. Same actually goes with the graphics card.
I'd agree with BudgetGamer12345's upgrade recommendations, but I doubt you will be able to overclock that Packard Bell System. I'm fairly certain the BIOS has been locked down to prevent that.
-Wolf sends
Edit:
Motherboard Specs