Seems your transmission is in failsafe mode. I would check the powers and grounds, especially the ones that go to the transmission. It should have a power wire that goes to all the solenoids and then the computer grounds the individual solenoids to achieve this shifts. No power no shifting except for park, reverse, neutral, and second gear.

To be clear you have the 88 Astro van with a 4.3 TBI, 4L60E, and have just swapped the harness and computer from a 2002 Blazer?

HTH Jeff