Since you mentioned that the car is weak without jumper cables, make sure that both battery cables are clean and secure at all ends. You might want to pull the battery and have it tested at autozone or oreillys.
Since there is no spark, the ignition control module, the coil, or the ignition switch are likely culprits. Your car must be an EX with an internal coil. Use a thin paper clip to jump the service connector to see if the ECU has any codes stored. Follow the instructions here http://www.dhost.info/accordinfo/howto/cel.html
You two-pin connector is brown. Post any codes that you find.
To test the ignition switch, pull the two pin connector going to the distributor. Turn the key to the II position. Test for 12V from the yel/blk wire to ground.