sorry for delay.. I have two ideas.
Once is check the event log on the pc after skyrim crashes, what is the error log if any.
how to get to error logs:
Open Event Viewer by clicking the Start button
, clicking Control Panel, clicking System and Security, clicking Administrative Tools, and then double-clicking Event Viewer.
If you're prompted for an administrator password or confirmation, type the password or provide confirmation.
You will see an application log on the left, select it and a list of stuff on the right..
So say at 11am you opened Skyrim and it crashed at 1105am, if you check the event log from 11am-1107am and look for something says error (will have a red icon to it). Or will also say Skyrim.exe (if that is the exe for the game.)
If there are errors associated around the time frame, what are they? You can double click on the event and see what it says.
2nd idea:
You mentioned that you uninstalled the game and re-installed before? But did you rename any folders in c:\program files that is related to Skyrim? For example, some games when you uninstall they only remove the main bulk of the game but leave all the config stuff. So you re-install and actually you're just re-using the broken pieces. This would require some digging when the game is installed and then uninstall, check the same locations to see if those folders are gone.
My guess would be somewhere around here:
C/program files/Bethesda soft works/skyrim
I would also do a pc search for file/folder with the word skyrim. Each folder I find I would rename to _old at the end of the name (exmaple: skyrim_old) by right clicking on the folder and choosing rename. Once all the locations are renamed, I would install the game again from start.
*remember only rename folders AFTER you have uninstalled the game like you normally have done.