Tips for Analyzing Circuit with Transistors
The first thing to do is to redraw the schematic with a more logical layout.  Put positive power at top and negative power at bottom so that current mostly flows down the page.  Then arrange signals so their logical flow (more like cause to effect, not current flow) is left to right as much as reasonably possible.  Feedback signals are exceptions in that they should go backwards because that is their purpose.

When you follow basic rules of schematic layout, not only will the circuits become more clear but you will after a while recognize common subcircuits.  This is a good thing to get used to, and it will also help you get assistance from others that are more experienced.

The circuit as you show it looks like a mess to me because I have to think about what is connected to what and can't just "see" what is going on.  In this case, just rotating the whole thing right 90&deg; is all it takes to fix it:



The writing is now sideways, but we can see the circuit from the schematic more readily.  

Since this is a homework problem, I'm not just going to give you the answer.  However, I would start with a few simplifying assumptions.  For example, assume all transistors have "high" gain.  Analyze the circuit as if each had infinite gain.  They don't of course, but the difference between a gain of 100 and infinite shouldn't change the answer much.  Also good transistor circuits only need some minimum gain from each transistor and work all the way up to infinite gain.  This may sound like a difficult burden during design, but it's really not.  Look at most transistor datasheets and see that while minimum gain is specified, maximum is usually not.  Or if it is, it is a fairly sizable multiple of the minimum gain.  In other words real transistors vary a lot in gain, that has to be taken into account anyway.

Note that what logically follows from assuming infinite gain is that the base current is zero.  So for a first pass to see what is going on, your model of the transistors is that they drop let's say 600 mV from base to emitter and don't take any base current.  You should be now be able to figure out the base voltages of T3 and T2, and from that their emitter voltages, from that their collector currents, and from that the remaining voltages.

Now if you want to you can use that as a starting point and modify things assuming some finite gain, like let's say 50.  You will see that the various voltages and currents won't be all that different.  If this circuit actually used transistors with a minimum guaranteed gain of 50, then the two sets of numbers you get represent the limits of the operating range, with most real instances being somewhere in between.