Akumanotou Tower of Demon (478kb no install version 1.00 made 2002) is a simple action platformer similar in style to Mario. Collect all the coins to progress to the next level. You do have a time limit which doesn't really matter in the early stages but will test you in the later stages. The game will try to connect to the internet when you load the game, just deny access and away you go.
Controls
Arrow keys for movement
Shift key to jump
Homepage (Japanese site)
http://www2u.biglobe.ne.jp/~nemojun
A handful of other games for you to download and try at this site too.