Okay, this game is pretty much like any other fantasy side-scroller, which is already a pretty bad start. And I was about 3 years old, so I obviously barely remember anything, but this is what know:
The character was a guy who had a robinhood-esque had, kinda like the guy in King's Quest (I know it wasn't any of those because your movement was only 2D, unless one the King's Quest games was just 2D). I'm pretty sure it was only 16 colors. You started in a room with no way out, and the only way to open up the passage on the right side of the screen, most likely by solving some sort of puzzle that I didn't understand, so I did stuff until I guessed it right. Then I can't really remember everything after that, but you eventually got to some kind of dungeon with spiders that came down (I'm pretty sure) and lil' green snakes that you had to jump over.
It's probably older than 1991, so just say anything that matches that criteria and I'll download it to check if that's it.
This has been bugging me for years because it's the first video game I ever played, so thank you SO much if you can tell me what it is.