This page describes a direct PIC-to-TI85 connection (it's quite simple, actually). No source is given unfortunately, just the .hex

This dude is also trying a similar thing.

This page describes the low-level protocol, and this page describes the higher level protocol.

It is definitely possible to "remotely control and/or view the screen on a TI-86.

Various VT-terminals exist. Some of them are Telnet 83, FTerm, RTerm, RTerm 83, ZTerm. Apparently they have semi-specific requirements (grey graphlink cable, 9600 baud), but other than that, you plug in the graphlink cable and it's a standard serial port.

If I can hook directly to the output port, it doesn't have to be 9600 baud, it can be any arbitrary rate, and the whole setup would be smaller/cheaper. This document gives a very good idea of what the Graphlink cable does.

The cradle for the thing has a serial connection, and presumably transfers data through the IR port.

Not being terribly popular, a brief scan didn't reveal anything about the IR protocol or possible terminal software, other than that the IR supports IrDA which may have some pertinent standards.

A most obvious choice. Short/long PalmPilot serial cables are readily availble.

And there's at least 4 VT100 programs out there, if not more.

There are probably several of these out there, but this is one of them.