When I am in the View Transactions window of the General Ledger module and I double click on an account to get the details of the account balance and then double click again on a specific transaction to open the window that shows me the details of a specific entry/line item, those windows open at the very top of my computer screen and the top half is cut off from view.

Each time I drill into an account like this i have to move and resize the window that gives me the entry detail from the top of my screen down into the middle of my monitor so that I can see all of the information.

Is there a way to permanently change this so that these windows open in the middle of my screen each time without constantly having to move and resize?

File | User Preferences | General disable "Save window position".

User Preferences is greyed out. Does that mean my user rights are limited and I need to contact my IT department to give me the permission to change this setting?

Yes.

And tell your IT department that there is no reason to prevent a user from changing their preferences.

In the interim, you could try Window | Original Sizes.