How do I change the rear gear ratio in my 1989 Corvette. Will it effect the computer and speedometer

There is a formula that you take your rear gear ratio, your tire size, & the number of teeth on your drive gear in the transmission. It will tell you how many teeth you need on the driven gear that attaches to your speedometer cable. Here is the address for one of these calculators.
https://www.tciauto.com/speedometer-gear-calculator

Assuming the tires are close to standard (i.e., 275/60/R15), this means you probably have a 4.11 ratio rear end in your Corvette. This was a very popular ratio on Chevys for drag racing. For highway driving you would want a higher speed ratio, such as a 3.55 or 3.36 ratio (or even a 3.08), depending on what is available. which would give you 70 MPH, 75 MPH, or 80 MPH at 3000 rpm.
You'll need to change the speedometer driven gear in your transmission for your speedometer to be accurate if you change the gear ratio.

Do you have any codes in the ECM ? Have you checked the neutral safety switch ?

For starters, you have to reprogram the computer or the speedometer will be off.

Did you replace the speedometer gear so it reads correct. mileage may not be affected as much as you would think. The ECM is calibtaed for the rear axle ratio.

The only way to accomplish that is to change the axle gear ratio. Trucks are generally geared for hauling, towing, plowing, etc, so you have more torque and power at lower speeds. If you change the axle ratio,your low end performance will probably suffer (sluggish acceleration at low speed). Basically, your T100 is not designed for 70mph highway driving.

There is no one stock speedo gear in a Chev. It is dependant on the combination of rear end ratio, transmission and tire size. Each car has the potential to be different. Theyare easily interchangeable. There is a small bolt holding a clamp where the speedo cable goes into the trans. Unbolt it and the speedo gear pops right out and slides off the end of the cable. If your speedometer is too slow put a bigger gear on, too fast needs a smaller one. It's trial and error but I think each tooth difference is 5 MPH, it's been awhile. Hope this helps.

If your gear set is worn, replace the differential with one from a scrapyard.
It is very expensive and an exacting science to set new gears up. if noise is from either carrier side bearing it is possible to replace them but generally if there is debris inside the unit the pinion bearings will be affected as well, requiring re-setting of gears. Depending upon what you ask from your vehicle, this is a good opportunity to change ratios. If you don't need all the bottom end performance, you could opt for a 3.23 ratio. If you are looking for more "off the line" power then go to 4.11's. Don't forget though that anything but the exact match to yours will require a speedometer drive gear change .You cannot stop the noise without making a repair.

Taller tire have more centrifugal force because they have more mass (weight). A body in motion tends to stay in motion. They also have a larger outer diameter therefore through all the weight to the out side of the tire. requiring more energy to accelerate and more energy to slow down than a smaller tire at the same speeds. This is why I would recommend up graded in your brakes and also lowering your gear ratio( numerically higher) if you are going to larger tires. A lower gear ratio will act as a torque multiplier which will get you moving faster up to speed and also adjust your speedometer to be more accurate.
When you go to larger tires your speedometer will be inaccurate because taller tire have large outer diameter. A taller outer diameter tire will travel farther per revolution than a smaller tire. This cause your engine speed to be lower with taller tires because your vehicles tires are moving slower do to it larger outer diameter.
There your vehicle can be re calibrated through the computer. 4wheel parts offers parts call true speed sensors which also recalibrate your speedometer accurately that is the way i would go. Also maybe up grade to larger master cylinder off a 1 ton Chevy and go with some drill and slotted rotors. You most likely will have better braking with these upgrades than you would stock. keep it safe!

Good luck and have fun.

check the fuses, mine did the same thing, I replaced the fuse in the fuse panel and it works great now.. easy fix