Trip odometer button not working

Were any lights (headlights, parking lights, DRL's) on when you tried to do the reset?
They have to be off for it to reset. The trip meter also needs to be displaying Trip A.
If they were not on and you started with the doors closed, key off, held the button down, turned the key on and held it in for fifteen seconds.
Try it a few times, as it may not reset on the first try.
The other option is to use a scan tool to reset it.

Okay, the button itself has failed. That could be a bad solder joint or failed switch. It pulls a line on the gauge cluster CPU to ground to toggle the readings and reset the warning. If the other warning lights come on during the bulb test and the odometer is working it is not the ground that is the problem. It is the switch itself. You have a couple options, remove the instrument panel, strip it to the board and repair the switch by soldering in a new switch or repairing the old one. Or you could get a replacement, but they are not cheap.
Another option might be to buy a DIY level scan tool that can turn off the light. That would also let you scan if the CEL comes on. Just be sure it can do that before buying.