A picture displayed at 1280 x 1024 has an aspect ratio (width x height) of 4:3. Regardless of resolution, most current monitors display an aspect ratio of 5:3 (wide screen).
Your laptop displays a maximum of 768 lines. A standard 5:3 aspect ratio would display 1280 x 768, which means your display is slightly wider than standard that standard.
This means:
1. The highest resolution your monitor could display with an aspect ration of 4:3 is 1024 x 768. It cannot display 1280x1024 under any circumstance.
2. To display your software at 1024 x 768, your laptop video system would have to allow setting it to that ratio, which would include black side panels, or you would need some after market software that could do the same thing. Preferably, that setting would be applied only when specified software was in use. Otherwise, you'd be resettting the aspect ratio every time you switched between applications requiring different ratios.