You should still have a mechanical speedometer. Near the back of your transmission is a cable going into the tailshaft. Unbolt the retaining clip and slide the gear out of the tranny. Inspect it for broken/missing teeth. You can obtain a replacement at any parts store, just know your engine/trans type and your rear end gear ratio. It could also be a bad ground at the speedometer itself.
The 1987 Chevy Celebrity uses an electronic speedometer, there is no speedometer cable. Assuming your speedometer has failed here are some possible causes: The VSS. vehicle speed sensor, may have failed. The speedometer may have failed. The ECM, engine control module aka computer, may have failed. There may be wiring issues such as unplugged, dirty connections, broken wires, etc.
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