Inspiron i3-2100 to i5 or i7 upgrade

Good evening everyone.  I am trying to get another year or so out of my Dell (used primarily for gaming) and I am at the point where I would like to upgrade the current i3-2100 2 core 3.1Ghz CPU to an i5 or i7.  I currently have a Dell Inspiron 620 (well out of warranty - so no worries of that).

I currently have the following:
- Intel 6 series C/200 Chipset
- Windows 10
- AMD Radeon HD 6900 (upgraded)
- Antec 620 Watt  (upgraded)

Question:  Can I use ANY i5 or i7 Sandy bridge (LGA1155) processor?

All the research I have done leads me to believe that the only reason I couldn't upgrade to any i5 or 7 sandy bridge processor was 65w vs 95 watts.  Considering my PSU upgrade needed to run my GPU that should not be a problem correct?  Unless there is a Dell motherboard limitation that I have not discovered.

Thank you in advance for your help.