please explain what the difference is between modprobe rt3562sta and rt2800pci
rt3562sta is the compiled from source code driver that wouldn't compile for you. We might have been able to work out the method, but why? The native driver rt2800pci works for you with no compiling.
how do you know? How would have I been able to find the answer?
Become a driver monkey by studying such things for 10-12 hours a day for ten or so years. No-one expects anyone to do that; that's why there is a forum where you can tap into the OCD sickos who love this stuff and then retreat before you get the rash.

The native driver may be blacklisted, the usual process when you compile a driver. Please check:
sudo gedit /etc/modprobe.d/blacklist.conf
If there are any 'blacklist rt2800pci' or similar lines in there, remove them. Proofread, save and close gedit. Now let's get rt2800pci to load on boot automatically:
sudo gedit /etc/modules
Add one thing at the end:
Proofread, save and close gedit. Reboot.

Now does your wireless work as expected automatically? If so, use thread tools at the top to mark Solved, so the searchers can learn and then retreat before you get the rash.

Seriously, if you need further assistance, post back.