My fuel pump relay (on the 190E) gave me the exact same problems. I could hear it clicking when ignition was switched on, but sometimes the fuel pump would not run with it. After finding out a replacement was £75, I opened it up, found a broken joint meaning the relay could switch, but the voltage would not travel out to the pump, and resoldered it. Works perfectly now for last 6 months.
Try listening for the fuel pump when you switch the ignition on, should whirr for a second or so.
2.5-16v 1990 90,000m Astral Silver
2.0E 8v 1986 107,000m Black