93 Civic Si, and when I go to pull my e-brake, only one wheel locks up. I've tried turning the nut to get some adjustment from the brake bias plate but still no avail. Is there a way to adjust the cable from the brake end? Or anyone had a similar issue and have a solution?

 

You can adjust the threaded rod behind the drum (assuming you have drums in the rear). Don't adjust them out too far or you'll drag your brakes constantly.

EDIT - excuse my ignorance - missed the "SI" part.

 

more than likely you have a seized slide pin, seized ebrake cable, or broken ebrake assy on your rear caliper. easy way to find out . Disconnect the pin that attaches the ebrake cable to the caliper have someone pull the ebrake cable to see if it moves. If it moves the cable should be okay. now your down to the slide pins or the mech. you will need to remove the caliper mounting bolts try and move the slide pins if they don't move and are stuck. then you need to heat them up to break them free replace the pins and rubber pin guides and use a good pin lube on them. The last one will have to replace the caliper and that isn't going to be cheep they are around 120 with a 100 dollar core charge. trust me I have had my 93 since new and have had to do this many times. I now clean and relube the pins every year.
Good luck