My MSX machine just died. Is it final, or can it be fixed?
Similar test as Caps Lock response: with audio output connected, type CTRL-G a few times - on a working machine that should give a short beep.
- Is it realistic to try to revive it?
- What other tests I can do?
- Are there any online resources that I could use?
Depends on what's broken, what means/knowledge you have available & value of the machine. Usually the difficult part is getting someone who knows a lot about MSX hardware internals, machine & equipment together. A forum like this is a way, but not optimal... 
Dont know this MSX Hitachi H2 personally, is it an MSX1? MSX2? Maybe you could take a photo of its mainboard so that we know what's on it?
If power LED lights, but Caps Lock doesn't respond, it's likely a CPU / ROM / RAM / MSX-engine issue. If any of the IC's are in sockets, a simple thing to try is pull these out & re-insert in the IC socket. Of course with power off, and be careful that you place IC's back the same way! Also: do you have any external RAM cartridges?
type CTRL-G a few times - on a working machine that should give a short beep.
Tried it, and there was no sound.
Depends on <...> what means/knowledge you have available
I could get (and I know how to use 
) most of the necessary tools: oscilloscope, multimeter, etc. As for me, being a programmer, I have an intermediate knowledge of electronics. And a collective power of knowledge of fine folks at this forum.
value of the machine
Well, it's priceless for me, seriously. Being a hobbyist / fun of MSX and all that... But you know what I mean.
is it an MSX1?
Yes, it is MSX1
Maybe you could take a photo of its mainboard so that we know what's on it?
Here, someone has already posted exact same machine earlier, but I will make more pictures myself:
imageshack.us/f/268/cimg7513.jpg/
do you have any external RAM cartridges?
Yes, I do. I tried to insert them and re-boot the machine.
Wait a minute... Haven't I seen that mainboard somewhere before?
Some fella from Japan tried to sell his stuff, this was his photo. he misteriously disappeared, though, you can see the thread here: www.msx.org/forumtopic13538.html , but I have nothing to do with him other than I tried to buy his Hitachi. :)
Anyways, here are some more (mine) photos:
https://picasaweb.google.com/111314133182937932580/MSXRepair?authuser=0&feat=directlink
If absolutely nothing is happening you may be missing +5V.
I will dig out my multimeter to check the voltage at the power supply and on the logic board and post the results here.
Brief symptoms, again:
- CTRL-G and Caps Lock doesn't work,
- power led is on,
- embedded cassette recorder works (rewind, play etc), and there is normal sound when the cassette is playing,
- monitor screen turns black when computer turns on.
Just checked the voltage: +5v exists. 
Just checked the voltage: +5v exists.
That's measured on the main board itself, not just @ the power supply?
I could get (and I know how to use ) most of the necessary tools: oscilloscope, multimeter, etc.
With "get" I hope you mean "use/borrow", not "buy for this occasion" ? 
At this point it would be very helpful to know what's going on at various Z80 control signals. Especially the Z80 clock input, but also signals like /MREQ, /RD, /WR, chipselects at the ROMs (pins 20 / 22), and RAMs (/RAS, /CAS). I myself have a homebrew logic tester I'd use for that, which has a small piezo buzzer that gives an acoustic indication of frequency. If you're willing to dig something like that up, it would help. An oscilloscope is even better, but perhaps a bit overkill for simple diagnostics. Another thing you might do is switch machine on for a few minutes, and feel with a finger if any IC's on the main board become suspiciously hot. As for suspects:
PSG: probably would garble sound, but computer should still work.
RAM: could cause dead machine, but you tried with external RAM & that didn't help.
ROM: possible, but in this respect old EPROMs are more often problematic than factory-made ROMs. And if a few single bits fail, chances are the machine would still boot.
8255: not a very complex chip, doesn't get hot under normal operation, usually very reliable.
Z80: dead ones do happen, but it's quite rare (usually results from something inserted into cartridge connector while powered on).
glue logic (those little 74xx chips in between): possible, but normally very reliable.
IC socket contacts: no sockets used here AFAICT, so doesn't apply here.
Videochip: runs quite hot under normal operation, in most MSX1's I have they're half dead. Normally also supplies Z80 clock so when 'dead enough' that would also cause things like Caps Lock response to fail.
The latter normally has a cooling plate on top, which is not installed on this machine's VDP. So if I'd had to take a gamble, I'd put my money on the VDP @ this point. Should that turn out to be the culprit: do you have a replacement for that?
Btw: what's that 40-pin chip between Z80 (Sharp LH0080) and 8255?
