my buddy had a similar problem with his 93 integra GSR.... we replaced his Ignitor (it's inside the distributor cap) and then we took out his weak internal coil and replaced it w/ an external coil (because the Coil on most hondas are very weak...especially internal coils)
slapped the sucker back on and started right up!

oh yah... we changed his cap and rotor while we were at it but you can just get away w/ a ignitor and/or a new coil.
test both and one should be F'ed up.....