Someone help rouguetubes. I need to listen in, as I have pretty much the same problem. it's keeping me from doing any upgrades at all, becuase they seem futile, given the crappy power.
Sounds like you do indeed have terrible power. First, try lifting the grounds on the various pieces in various combinations using cheater plugs. This is very cheap and may at least improve the hum problem. Most simple surge protectors won't do much. I assume you're not able or willing to do any wiring changes, so you may be looking at the PS powerplants or similar if you want to really solve it.
You need to begin with some analysis of your current. It sounds as though there is too much on one loop if the lights are dimming when the equipment is turned on. The hum on the speakers sounds like a ground loop. Find out what appliances are on what circuit loops and whether any current loops are shared with other apartments. If it's an old building with old wiring and there is really no hope, I'd talk to the superintendant and see whether you can install a separate dedicated line to the main panel at your expense. An electrician can do this without breaking the bank, and it would be the best place to start.
Check out Sutton Designs NETSavers line conditioners (models LC600 and LC1250 ):
These are not necessarily designed for audiophile use, but they provide clean, stable power at a very reasonable price.
Lifting the ground is a bad idea. What you need to do is isolate your system from the house. This can either be achieved by using a isolation transformer like a Plitrom Medical Grade Type 1 or by using a balanced transformer (60/60) (BPT, Equi-Tech, etc). In either case make sure you purchase a transformer that not only handles the max load of your system but also has a little extra because all transformers convert energy to heat. So to make sure dynamics are not restricted I would look at a transformer 25% to 50% larger than your system needs.