Weird cooling system behaviour

just my guesses.
1. the brown crap is stopleak.
2. the radiator and heater core are probable shot
3. the stopleak has plugged your engine and you will have to flush several times after you get the new heatercore and radiator in
4. All this is going to be expensive.

Why guess when you can read a few posts back and see that you're right?!

As stated b4, rad is shot and I have a new one. Heater core leaks and I'm going to circumvent it untill I source a new one.

Expensive is a relative term. Sure ain't cheap.
Good call on the brown crap, hadn't thought of that...

Why clean the passages with a new rad and core in place? That will just get them dirty too!

How do you (all) advise I do a full flush of my engine block with the following limitations:

It's parked on a city street. (thankfully in front of my house) No garden hose, no high pressure hose.

I was thinking:

Top off the cooling system incl. a half can of system cleaner (no rad, so less cleaner)

As the rad is out I could use a longer piece of flexible rad hose and connect the bottom and top rad in/out directly. Run the engine for 2-3 minutes, drain all fluids and repeat process untill clean. Perhaps, carefully, disconnect the bottom hose to drain, have an assitant start the car and let the pump help get the gunk out, cut engine as soon as flow diminishes...

I wan't to do it this way so I don't en up possibly clogging the new rad etc.

Sound good? Should I do this with or without my new T-stat in place? (pressure wise)