Give musagi a try.
It's very NES-ish, piano-roll based (and not a tracker), so it is more intuitive to use. It's free, lightweight and relatively powerful.
It does have a tricky initial hump in terms of learning curve, but then it's pretty easy to do stuff.
BFXR / SFXR are both great for sound effects as others have mentioned.
I'll add in Musagi:
http://www.drpetter.se/project_musagi.html
It's like a very lightweight (and free) DAW that is super easy to use with just your mouse. You can get free VSTi (virtual instruments) to load into Musagi here:
On a side note I also use Magix Music Maker 2014 with some loops (ambient, movie score etc) that I purchased for commerical use. Much more expensive route but very handy for those that aren't instrumentally inclined.
Try Musagi. It's free, easy to install, but it's not that easy to use. Have a look at it anyway, it's a tiny download and there are some tutorials online.
Old video game music is usually composed of four different wave-forms. Sine waves, square waves, "triangle" waves and noise. Each of these wave forms are used for different instruments in old games, for instance, "noise" is usually used to mimic drums and sine waves sound nice and mellow, so they can be used for melody and harmony.
That may be a bit low-level, so maybe I should just point you to something like Dr Petter's Musagi and you can play around with the different instruments yourself.
Everybody suggesting complicated and high-end software for producers and professionals, you don't always need that. Sometimes what you need are simple easy to use music creating software. Here are some:
After making some music you can always export track by track and mix them properly or apply effects, or play it live with pxTone inside your game.
The entire Cave Story (original) soundtrack was made in PxTone.
Musagi. Maybe not as 'legit' as lsdj or famitracker, but you can make chip sounds with it. It was developed by the guy who later made Sculptris and ended up working for Pixelogic on Z-Brush. He no longer works there, tho.
http://www.drpetter.se/project_musagi.html
If you head to the forums on that page, there's a section for Musagi. A while back Dr Petter released the source because he was busy with Sculptris and could no longer update it. Someone took it upon themselves to update it and he added quite a few features as well as stabilized it a bit more. Definitely check out that version. There are also a number of examples of tunes made with it. It's maybe not the most advanced thing on the planet, but it's super easy to use. It does have a few quirks to it, tho, and a few bugs that never really got ironed out.
He originally designed it to make music for his games, and you can get an API for it to use the tracks in games and keep all the loops and whatnot working. He's used it in a few of his little games projects.
Currently he's working on a 'sequel' to it called Paramole that looks interesting, tho is probably a ways off from having a public release.
Thank you! 4:51 is Musagi and I'm not sure what you mean at 4:38? Programs I used include: Photoshop, Flashdevelop, Musagi, Bfxr, Audacity (for conversion)