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Hi, I'm Mike G and I'll be assisting you. Tell me the way the switches were wired. I need to know the number and colors of the wires.
The wire that was on the black screw is the common and when attached to only one of the others will allow the other switch to work. The unused wires should be capped.
If you have 2 switches controlling a light they are 3 way switches. The way they work it a common wire is switched between 2 traveler wires. Onel one will be hot depending on the switch position. At the second switch you have the 2 travelers and as stated only one is hot depending of the first switch. At the second switch the common is hot depending on the position of the switch. The action between the switches allows for turning on or off the light from either switch. By removing one of the switches and wanting to operate the light from the remaining switch, you connect the common (on the black screw) with one of the travelers (on the gold screws). The unused wire is capped.