I would think it would be best and easiest to just check the fuel pressure is in the car. You would have to disconnect a fuel line under the hood and connect a pressure gauge. Then jumper the relay to test the pressure. No a trickle is not good! There is a spec for the pressure. I don't know what it is but you can look it up somewhere. It seems that you have a bad fuel pump. However, look up the spec and do a proper test or have a shop do it. Then you will know for sure.

So anyone have the numbers on the fuel pressure?

I logged on to Chilton through my library (you likely can do the same), They did not have info for the '89 but they had some info for the '92 190E. Here is what they say for fuel pressure test:

"Disconnect the fuel line at the fuel distributor and connect a pressure gauge 103589002100 or equivalent, to the hose.

Connect an adapter 102589066300 or equivalent, to the plug fitting at the fuel distributor.

Jump the fuel pump relay at the manifold and check the pressure. If not within specifications, check the fuel filter and pump pressure at the pump.

Disconnect the pressure line at the fuel pump.

Connect a pressure gauge and adapter to the fuel pump outlet at the pump. The pressure should be 29–58 psi (2–4 bar).

Reconnect all fuel hoses and check for leaks."