The Palm SysRandom RNG was reverse-engineered by Ian Goldberg and documented e.g. in this Password Generator exploit:
/* The PalmOS SysRandom() RNG. */
static unsigned int multiplier = 22695477;
static unsigned int _seed = 0;
short palm_rand (unsigned int new_seed)
_seed = new_seed;
_seed = (_seed * multiplier) + 1;
The problem is the HTTPS today. There is a huge push to migrate off of HTTP and on to HTTPS. But older machines simply can't do the necessary encryption in time.
But much of this can be mitigate off-device by routing through a proxy that takes HTTP traffic on one side (device side), and talks HTTPS out the other (internet side). It's not drag and drop, but ...
For web pages, you can use the Web rendereing proxy, displaying modern web pages inside a GIF and imagemap. It works well, though Google Captcha often thinks (rightfully) that it is not a human controlling the web browser and won't let you through.
For pretty much anything else, you can try to locate a VNC client for your platform, There are clients even for ...