If the limit really is in the card, you can almost certainly get the higher resolution by reducing the number of colors. I expect you have 32 bit color. I don't know if 24 bit color would work. I expect 16 bit color would work and get the desired resolution.
More likely, the card can do the desired resolution even with 32 bit color. It just needs an appropriate modeline in the xorg.conf file.
The important info for figuring this out is usually buried in
That is likely rather large for posting the whole thing (though maybe it is OK). Even an expert might have some trouble picking out the details that explain a given problem, but see if you can spot and quote some chunks of that that seem related to this issue.
I just grabbed the /var/log/Xorg.0.log of a server here (where no one even cares about the local display) and chunks that would have been relevant if we had a problem similar yours are surprisingly obvious:
(--) NV(0): VideoRAM: 131072 kBytes
(==) NV(0): Using gamma correction (1.0, 1.0, 1.0)
(WW) NV(0): config file vrefresh range 50-180Hz not within DDC vrefresh ranges.
(II) NV(0): Monitor0: Using hsync range of 30.00-95.00 kHz
(II) NV(0): Monitor0: Using vrefresh range of 50.00-180.00 Hz
(II) NV(0): Clock range: 12.00 to 400.00 MHz
(II) NV(0): Not using default mode "1600x1200" (hsync out of range)
and similar stuff further on, such as
(WW) (2048x1536,Monitor0) mode clock 266.95MHz exceeds DDC maximum 240MHz
So we get to see how much video ram is available (the primary limit on an older card supporting a higher resolution) as well as the horizontal, vertical and pixel timing constraints that the driver thinks it is subject to, as well as some resolutions it rejected and why.
Typically the driver is confused about the true timing constraints of the monitor and that can be overridden in xorg.conf. Or maybe some timing constraint of the old card is too low for a standard modeline for the resolution. But LCD's tend to do quite well (unlike CRT's) with lower refresh rate. So if the card has low timing limits, you can get it all to work by selecting some non standard lower refresh rate.
Earlier in the log are some details maybe useful to experts, such as
(II) Primary Device is: PCI 07:00:0
(--) NV(0): Chipset: "Quadro NVS 285"
You can get that part from lspci as well, but I don't think the parts you can get in lspci are as good for solving the problem as finding the right parts of that .log
Once you figure things out from the right parts of that .log, you would edit /etc/X11/xorg.conf to fix it. Probably you should post what you have there to begin with in order to get advice on what to edit.