Blowing up TNT in Minecraft classic
Solution 1:
You can't detonate TNT in Minecraft Classic. Redstone, and indeed exploding TNT, are features that were just not implemented at this point.
The block is there, but if I remember correctly, the functionality of activating it by punching was added in the Survival Test version, i.e. the version directly after the current Classic version. Redstone was also added at a later date (Alpha 1.0.1, according to the wiki).