teceem: Like ZFR said; install the driver for your graphics card or chip and look for the setting in its control panel.
Sometimes it's not possible at all - like with some older(?) laptops with integrated graphics.
The last laptop I had which didn't support this on integrated graphics was over ten years ago, and even that supported "centred" graphics (i.e. 1:1 pixel mapping with a large black border).
Pre-post-edit: Ah, I see the OP is using a graphics card from 12 years ago... They might be out of luck then.
saisaaseda: Yup, it's a pain in the ass. The Blackwell games (Legacy, Unbound, etc) even have an actual option in the game's own settings to play it with black sidebars without stretching it, but checking that box doesn't do anything at all, even though the games were made around the same time as my PC and monitor...
I've been playing AGS games for years and years and I've never known that "sidebars" option to work unfortunately.
Is buying a newer but still quite old graphics card out of the question? You'd probably be able to get something that's a massive improvement for not very much money.
saisaaseda: Radeon HD 4850 with Catalyst 13.9
Not a lot of settings to work with as you can see :)
Just a thought: What outputs does your graphics card have on the back and what inputs does your monitor accept? I seem to remember "maintain aspect ratio" being disabled on many cards when connected via the old analogue VGA cable. Using a DVI or HDMI cable might be a possible fix.
teceem: Maybe it's not possible in your case? I don't know, the last time I had a monitor with only a VGA connection, it was a CRT monitor.
Ditto. I find it strange that the problem is caused by a new monitor, but the new monitor only has a VGA connector. 0.o
HunchBluntley: - I know DOSBox has a setting to keep the original aspect ratio, but if your monitor and/or GPU software don't cooperate, it will be unlikely to work when playing the game in full-screen mode
Actually, the aspect ratio option in DOSbox is for a
different problem. However it's pretty easy to get DOSbox to add the appropriate sidebars by specifying your native resolution for fullscreen.