Welcome, you come right place.
Join us at
https://www.eevblog.com/forum/testgear/restoration-glory-of-keithley-2001-dmm/1. As first step - remove ALL electrolytic capacitors on analog board. Use low temperature for soldering iron (240-260°C) since there are no polygons and it's easy to peel off pads even with little overheat.
2. Clean all electrolyte on board with clean alcohol. In most contaminated parts best to remove components (desolder), clean everything and then solder back. Clean any flux after soldering.
3. Make few photos of cleaned board with damages, and get ready to spend some time to repairing connections. Beware via holes, sometimes they got open too. You can reference my schematics recovery project
here and
here for items in works4. After fixing damages, try to power on and measure power voltages. Check if anything heating up too much. If everything seem well, run selftest and check errors (MENU/GENERAL/TEST/BUILT-IN_TEST)
Or you can sell your 2001 to somebody who fixing 2001's in thread and need it, if you don't have time/wish to mess with lots of repair work.