Broken boiler vs. plumber
There are repair jobs, that almost anyone can do themself, but broken boiler isn't one of them. Boiling hot water and immense pressure - those are the things that define boiler, and also the things you should be wary of.
Calling in professional plumber isn't any shame in this case, it is necessesity. It is different from a ticking bomb, but close enough, especially if the safety valves are at fault. All in all, you need expert on this - let him do his job, and relax. He is aware of the risks involved and already knows how to avoid any mistakes. All you need to do is coffee and maybe some snacks, while he do his job.
If you are not convinced by this, and ready to repair you boiler alone, all i have to add is this: search the internet for movies of exploding boilers, I dare you.
Water isn't going in the outflow...
Even though we landed on the moon and are able to comunicate freely across the globe in real time, we still are sometimes stumped by mundane things like clogged pipes - what do we do then, in our hi-tech, modern times?
The same thing as always - call in the plumber. There maybe quicker and cheaper solutions, of course - but unless you are sure that drain cleaner isn't going to melt your pipes, or actually just do what it is supposed to, it is better to leave it to professionals.
There are some things, in the pipes, that you don't want to see - trust me on that. Besides, expert plumber can always recommend what to do, to avoid this kind of situation, and which products to use if need be.
Other than that, it usually takes something more sophisticated than a plunger, to get rid of the clog - if you even have that to begin with. So don't fret, or take this as an insult to your aptitude, and contact with plumbing services.
Is it worth it to repair a broken pipe yourself?
Manual repair is a way to get rid of the fault, which is used by many of us. Often it can be done very easily, but if they relate to the hydraulics, better be careful. It is not easy to replace a broken pipe or repair the faulty seal, because in this case a better choice would call good service hydraulic, who will do everything professional and efficient. Such companies can now find almost everywhere, so instead undertake to repair the personal risk and higher costs, it is better to entrust this task good art. It is they who fix everything as it should, without causing additional problems.