I have a Dell with a i5 2320 (Sandy Bridge) and have had no problems with 12.04. Before that I had both 11.04 and 11.10 installed on my old Dell 2.8Ghz Dual core built in about 2004 and had no problems with either of those so I'm not sure what problems you saw.
In 12.04 I would suggest:
mesa-utils will improve the display(mine was slightly too large for the screen without it)
libtxc-dxtn-s2tc0 will provide the texture compression library needed for
mesa to display some of the better games(Note: some games that need the s3tc compression will not load as they think that the card does not support it(Psyconauts is one) and must be forced in the terminal with
force_s3tc_enable=true (program) (even with that my GPU will not run Psyconauts but will force enable others)
Those are the only things I can think of so you should be fine installing 12.04 on your computer.
Note: if you have a non-integrated GPU(AMD,Nvidia, ATI) you will need to install the proprietary drivers for those and there are plenty of answers here on askubuntu. I will defer to those as I don't have any and have never had to install them. From what I have seen in passing, hybrid graphic cards require some work to get working if they work at all, but again I cannot verify any of those problems myself.