Your HP Mini 3500 netbook uses the Intel Graphics Media Accelerator 3150 graphics-adapter. There are no know GMA BIOS editors (you can only update the video BIOS by updating the system BIOS), so even if it were possible to do what you want with an Nvidia or ATI video-card, it won’t apply to your case. Sorry; netbooks just aren’t meant to be hooked up to widescreen LCDs.
Since your netbook is still new and supported, you should consider contacting HP to ask them to fix the shortcoming. You may not get the information you wanted to edit the video BIOS, but at least your problem would be officially fixed without compromise. There are several support options, so you should be able to contact a technical support rep. It looks like you have already asked other users about the problem, and like DimaO said, the specs (do a search for “resolution”) indicate that maximum resolution for the analog VGA connector is 1440x1050. That’s why HP blocked higher resolutions in the BIOS; because they are not supported and would have unpredictable/unreliable performance and/or results. Even it if works, it is not dependable and so they don’t allow it or support it. It’s the same with plenty of other hardware. For example, CPU manufacturers often produce a batch of the same CPU, but then lock it down in different ways to release different versions. Unlocking it may work, but because it’s a hack, it could cause problems, and at the very least, would void the warranty (which I suspect is also the case for your netbook; flashing unofficial BIOSes is usually a violation).
What do you mean by your first sentence? What exactly is the problem with the LCD monitor on the aforementioned systems? Are you saying that the LCD’s native resolution is not supported by the video card? There aren’t exactly dozens of unique resolutions; there’s generally a small handful, and those are generally supported by most video cards made in the past dozen years (ie, since LCD monitors started becoming affordable for the masses). The problem will usually be a combination of really old video card and non-standard LCD monitor.
If the mode is blocked, then it is not supported for whatever reason, otherwise they wouldn’t have blocked it; the mfgs are stupid or purposely messing with customers. Even if there is a way to force it to switch to that mode, then there is likely to be problems.
When you say that the graphics mode is not supported, do you mean that it is not listed in the list of resolutions in Display Properties (or other resolution selection dialog)? For example, 320x200 is rarely listed these days, and even 640x480 isn’t provided as an option in Vista+. If so, have you tried using a resolution program such as QRes or QuickRes to manually set the resolution?
As for the VESA BIOS Extensions, you are misinterpreting it. There is no actual video BIOS involved in that. Rather, they are extensions to the standard BIOS. That is, VESA extensions specify additional graphics modes that were not part of the original set of modes that the (system) BIOS supported via the
INT 10 function (which was used to set the graphics mode among other graphics-related things). So basically what would happen is that a video card mfg would build their cards to support these additional graphics modes, and thus, the card supported the VESA BIOS Extensions.