3458A reads around 1 V AC when input terminals are shorted. Upon applying some voltage, the value changes, but it's nowhere near the value it should measure. What could be the problem?
Since I haven't worked with this model of equipment I only have some points to check. If there is no error when doing the self test it should be working. Check if there is some offset stored Maybe there is a connection at the back end that influences the measurement
If the short reads close to 0 on DC, 2 wire Ohms is fine, you have done a reset and AutoCal but AC still drifts or is offset you are down to looking at the AC board. There may still be something else but the AC (A2) board is about he second most failed part in the meter. There is an Assembly level repair manual in the manuals section. http://cp.literature.agilent.com/litweb/pdf/03458-90011.pdf Fig 15 on page 45 shows the A2 board. Re-seating may help but I would not count on it. Good luck.
If there is no error when doing the self test it should be working.
Check if there is some offset stored
Maybe there is a connection at the back end that influences the measurement
or it could be damaged.