Although I haven't really studied the bct8 in detail, Uniden tends to stick with standard circuit configs. for a lot of their radios. Generally, 12 volts supplies the audio amplifier, feeds a 9v regulator circuit, and goes to a remotely mounted NPN transistor that controls the backlighting. The 9 volts is used in various locations througout the radio, and is furthur reduced by separate regulators for the analog and digital portions of the radio (say 3.5 volts or so).
Given this distribution scheme, we can possibly narrow down the source of the problem.
The fact that you have hiss audio, and backlight, tells me that the 9v regulator is probably fine, and the analog supply is probably fine.
The fact that the display doesnt work, and you have no squelch control tells me that the CPU isnt running/executing properly. The cpu is what usually controls the audio muting for the squelch, so if the cpu isnt running as it should, the squelch action wont work. This could be caused by a number of things. The primary suspects being the digital supply regulator (probably a Toko 11238 or similar), and the cpu reset circuit (usually a voltage detector IC, a few diodes and a npn transistor). Other possibilities include a bad/poorly soldered clock crystal, or even a trashed CPU(although I doubt that).
Aside from the transistor that controls the backlighting, most of these components are surface mount, and very small. Also, being near the CPU, they are possibly covered in epoxy. Not somehting I would suggest digging into unless you have experience in SMT rework/repair.
Does the radio react to the keypad at all? Does it make any beeping sounds? Or does it just light up and sit there like a dumb brick?