Video games are a common source of display problems, but if you are seeing the borders immediately upon booting up, it is not likely that unless the video game loaded a "permanent" driver or you are such a hard core gamer that you have the computer bootup in game mode. If the problem is any form of driver other than the required display driver, it would not be loaded in safe mode (actually, even the monitor-specific driver would not be loaded in safe mode). Bootup in safe mode and verify the the full screen is being used (reboot and hold down the F8 key). If that checks out, the problem is software. If there are any video games installed, that would be my first suspect.
You can try to spot candidate software using MSCONFIG. That lets you control what gets automatically loaded when you bootup. Click the Windows Start button (lower left corner), and type msconfig in the search or run window and hit enter.
On the General tab, pick Selective Startup. On the Startup tab, anything with a checkmark is loaded at bootup. Look for items that look like video games, video enhancers, graphics enhancers, etc. You may need to look up items on the Internet to see what they are. Ignore anything where the manufacturer is Microsoft. Uncheck suspect items (make a list of what you uncheck so you know what to put back later). Click Apply. On the Services tab, select Hide all Microsoft services. Again, the checked services are the ones loaded at bootup. Use the same process. If you accidentally uncheck something critical and the computer doesn't work right, reboot in "safe mode with command prompt", run msconfig, and put the item back or select Normal Startup on the General tab, click OK, and reboot. To see the changes, you always need to reboot after changing anything in msconfig because all it does is define the bootup process, not change anything already loaded.
The fastest approach is to identify a small group of candidates and disable them all. Reboot and see if that group contained the culprit. If so, restore the candidates one at a time until the problem recurs. When you find the culprit, just leave it disabled or uninstall the program. If that group didn't contain the culprit, add another group of candidates.
Another method you can try is using the Task Manager. Right click on a blank area of the tray at the bottom of the screen and select Task Manager. The offender will be on the Processes or Services tab. On the services tab, you only need to be concerned with ones whose status is Running. Click on the Status heading and that will select it as the sort order. Clicking it again will change the direction of the sort if you want to move all of the running services to the top or bottom of the list.
Using the Task Manager is immediate, you don't have to reboot. These are things actively running on your computer. If you mess up and the computer hangs or crashes, just reboot. What you disable is not remembered. It is the opposite of msconfig--any changes affect only that session. The goal is just to identify the culprit so you can disable it in the bootup or uninstall it.
The shortcoming of this method is that not everything can be disabled. A program can be causing problems but it or a replacement must be there for the computer to work. If you disable something and the computer stops working, you don't know whether or not it is the cause of your symptoms. Unfortunately, the problem you are experiencing is likely to be something that is performing a critical function. You will luck out if it is something like a game that is just "riding on top" and can be stopped without hanging your system. Don't be surprised if your attempt to stop something produces a warning message that the system may become unstable. If it is a candidate that you need to test, just do it. The computer may hang or crash but it won't blow up. Just reboot.
On the processes tab, look at the descriptions and look stuff up online if you are not sure. Click on the Image Name heading to select it as the sort order. Otherwise, the items will continuously bounce around as their resource usage changes and it will be hard to select what you want. To stop an item, right click on it and select End Process Tree, which will stop the item and anything else associated with it. On the Services tab, right click the item and select Stop Service.
You can get a little insight into items by cross checking. On the Processes tab, one of the right click options is Go to Services. On the Services tab, there is a right click option Go to Process. These will show you what is associated with what. Also, on the Services tab, there is a Services button at the bottom. This will open a window that provides much more information and explanation for each item and even allows you to change how each service starts.
These approaches are for starting "blind". If you have any video games loaded on the computer. I would start with them. Look specifically for the program names or publishers in msconfig or Task Manager.
One other thing to look for: your computer probably has some chips and software for handling graphics. Open the Device Manager (Control Panel, Hardware and Sound, Device Manager or Control Panel, System and Security, System, Device Manager; there are probably lots of other routes). Click on the arrowhead to expand Display Adapters. Right click on your display adapter and select Update Driver Software. This is another case where if all else fails, try downloading the driver directly from the manufacturer's web site and install it even if your system says the one you have is newer or up-to-date. If doing so produces new problems, you can roll it back to the previous driver: when you right click on the display adapter in Device Manager, choose Properties. On the Driver tab, select Roll Back Driver.
If none of this works, go to Lowes and purchase a large hammer...