When I was a kid, I went to my friend's grandparents house a few times and I vividly remember they had only one videogame system which was an NES and they had only a multicart with it. As I was only a kid at the time, I never thought much of it and for the life of me can't recall what it was called. Hopefully someone here can identify it? I'll do my best to describe it as best I remember.

The cart was definitely an NES sized cartridge, not a Famicom game with a converter. When you loaded it up, you were greeted with a solid black background with the game titles on several pages. On the left side of the screen there was the outline of a manly figure, which I'm almost sure is the exact same image from Power Blade 2 http://www.coolrom.com/screenshots/nes/Power%20Blade%202.gif.

There was also menu music, a slow paced tone that I've never heard in any other NES or Famicom game in all my years since.

The games themselves were your typical fare - City Connection, Circus Charlie, Battle City, Ice Climber, Duck Hunt, Super Mario Bros. In addition, there were repeats of at least Super Mario Bros. which did things like start the player on world 2-1, give invisibility, always give the player the fire flower, etc.

Given what I remember, does anyone happen to know this multicart? I'm hoping I can track it down and get a copy for my nostalgic memories.

Have you checked through the various Supervision carts?  That's the best place to start.  They pretty much dominated multis in the states.