My 2000 Silverado won't shift from second to third and the speedometer quit working. I replaced the shift solenoids but it didn't help. Any suggestions?

see if this link helps you out.... My 2004 chevy trailblazer won shift from second to third gear Google Search

Here is what the service manual says about the EPC solenoid, the processor looks at allot of different inputs to command the solenoids, such as Throttle Position Sensor, Vehicle Speed Sensors, Transmission Range Sensor and RPM signal, The PCM controls the shift patterns for the transmission. Electronic Pressure Control (EPC) Solenoid
The electronic pressure control (EPC) solenoid is located on the main control valve body and is controlled by the PCM. The EPC controls line pressure used to apply and release clutches and bands in the transmission.
The 2-3 shift solenoid is located on the main control valve body and is switched on and off by electrical signals from the PCM. The 2-3 shift solenoid activates the 2-3 shift valve which controls the automatic shifting between second and third gear. Second gear is established when the 2-3 shift solenoid is switched on. The 2-3 shift solenoid is switched off when vehicle speed increases and requires a second to third gear upshift.
The 3-4 shift solenoid is located on the main control valve body and is switched on and off by electrical signals from the PCM. The 3-4 shift solenoid activates the 3-4 shift valve which controls the automatic shifting between third and fourth gear. Third gear is established when the 3-4 solenoid is switched off. The 3-4 shift solenoid is switched on when vehicle speed increases and requires a third to fourth gear upshift.

your 2nd and 3rd shift solenoid are stuck open or closed and your over shift solenoid is the same

Time for a rebuild

You have a shift solenoid sticking its located in the valvebody.Pull the transmission pan off and you will the solenoids in the back of the valvebody they will have wires hooked to them.Replace the bad solenoid and the filter.

P0700 Information Code The Transaxle Control Module (TCM) monitors the malfunction of sensors and actuators relating to transaxle control. You will need to have your TCM code scanned to figure out what the problem is. Most likely it's a bad solenoid in the transmission. Most automotive shops have the TCM scanner.

I’m happy to help further over the phone at https://www.6ya.com/expert/jeremy_69f3cc28d95bf514

YEP YOU NEED VSS SENSOR HOOKED UP SO TRANSMISSION CAN SHIFT RIGHT.AND SHIFT TO OVER DRIVE AT SET SPEED. YES YOU NEED TO SEE YOUR SPEED TO KEEP FROM GETTING A SPEED TICKET.DONT UNPLUG IT.

A common issue are the input and output speed sensors.When bad they cause the vehicle to go into limp mode keeping it in second gear and speedometer sometimes no longer works.

this problem is a common failure associated with your shift solenoinds inside your tranny. of course a shop is not gonna tell you this because by the time you wanna get it repaired it is usually too late and have already cause damage to your clutch pack and internal parts, thats the main reason why a shop wont mess with just replacing your shift solenoid (aka valve bodie)

i dont think the two things are related check your speedo cable inner cable could be frayed or kink on outer cable if not disconect cable from speedo end and lube it