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This is what it took on my son's 2001 Z/28. Not sure if applicable back to 1990.
01. Turn the ignition ON (The radio displays LOC)
02. Hold down the Radio Presets 2 and 3 buttons for six seconds
03. The radio display changes from LOC to a three-digit number. Write this number down. Don’t take forever, fifteen seconds max before the next step.
04. Press the AM/FM button
05. The radio display changes to another three-digit number. Write this number to the right of the first one.
06. You now have a six-digit number, the first three digits are from STEP 03 and the last three digits are form STEP 05
07. Call 1 800 537 5140
08. Press 1 then # (pound). You’ll hear “Invalid Code, try again”
09. Press 620529 then # (pound). You will be asked to enter your four or six digit code followed by * (star) [IF THE "620529" doesn't work, try 206053, 202107, 106010 or 202108.]
10. Enter the number from STEP 6 then * (star)
11. Listen to the four-digit number and write it down. It will be repeated twice
12. Turn the ignition ON (The radio displays LOC)
13. Use the MN and HR buttons to enter the code from STEP 11
14. Press the AM/FM button. The radio display changes to SEC
It currently works. But I'm going to do some work on my car and will be unhooking the battery at some point.
If the radio is OE/GM still you will have no issues. You will loose clock and tuner pre-sets but all else will be fine. I've never attempted to power through a cigar lighter to avoid loss BUT a '90 I wouldn't waste my time/money. CLOCK and PRE-SETS for tuner.
Some dealers will help you unlock radios if they don't have to send to a tech to unlock it, and they are not slammed. As long as all LEDs light up they will rarely need a tech to unlock it. If you have owners manual it has procedure to set your own code. The factory back up code should still remain even if you forget the one you made.