[Problems with my 555 circuit]

Electrolitic? Already had power applied? It will explode once you turn it around and apply power.

You have the LED in backwards. If you reverse the LED the same thing will happen but flashes when connected to ground, and stays off or on connected to +V.

[Binary clock :)! Any one familiar with binary counters?]

I built my clock using decade counters and BCD-7 segment decoders.

Is this going to be a completely digital clock?
What are you using to make your oscillator? Be sure to put a schmitt trigger at the output of the timing circuit so you get rid of any bouncing.