I can’t say for sure what’s causing that problem specifically, but I do notice what may be an interesting console error:
downloadable font: OS/2: Bad sTypoLineGap, setting it to 0: -32 (font-family: "so-slider-pointers" style:normal weight:400 stretch:100 src index:1) source: https://www.portagewi.gov/wp-content/plugins/so-widgets-bundle/css/slider/fonts/slider.woff?8p86w5
It looks to be related to a plugin so-widgets-bundle — does deactivating that plugin change how the form is displayed?
Additional question: does deactivating SearchWP Live Ajax Search affect the button?