The 'bulbs' are LED's. The AC indicator LED probably burned out. I've never opened the panel, but my guess is the LED's are soldered to a pc board running the length of the panel.
The round opening to the left of the Panel Display label is a momentary push button. When pressed, lights the other LED's to indicate status of Battery charge level, Main (Fresh water), Black and Gray tank levels. The button looks broken. Again, my guess is the push button is also soldered to the pc board?
Both are easy fixes and parts should be available at your local Radio Shack. If you cannot solder, maybe someone at the store might be willing to do it for you, but I question the capabilities of most Radio Shack employees these days.
The pump light has no bearing on the AC Power LED or momentary button.
Hope that helps.