Is it a factory Toyota remote? Is the little red light also a button, or is it attached to a black plastic bracket? A lot of the ones that are attached to the black plastic thing have a little black push button on the back side of it.
And what exactly do you mean by "reset" the alarm? Arm it? Disarm it? Disable it?
Unfortunately, it sounds like the alarm module itself has failed. I'll be honest with you, it's a cheap cheesy system and I've seen a ton of them die. Your best option if you like and plan on keeping the truck is to get a good aftermarket alarm. The only brand I would recommend is DEI. DEI makes Automate, Viper, Clifford, Python, Avital, Boa, Rattler, and about a dozen other brands. They are all basically the exact same system with different 'brand' names. There's a reason for this, but kind of long and lengthy and I won't bore you with the details :) Anything made by DEI is good, and have an extremely low failure rate. 99% of problems with them is installation related, not equipment related. A good installer that knows what they're doing is key.
If you want to keep your factory remote, Automate makes a system called the AM1 that is a full security system that utilizes your factory key fob. Your other option is you could get any number of systems that use their own remotes if you don't mind getting different remotes. Plus it gives you the flexibility to add remote start, you could open your windows with the remote, or a ton of other things that you can't do with the factory system.
Good luck :)