It's too late, I already screwed up the trimmers and the tuning capacitor looking for the best signal, but I think I can alight it again.
That is very bad. Which ones you touched? Is at least the yellow one untouched?
If you messed up just with the red (oscillators) and the trimmers, it could be aligned using existing stations. First align the red oscillator coil for the station on the bottom end to match the scale, the "O" trimmer for some station at the top end of the band to match the scale, then in theory the antenna coil needs to be aligned at a station near the bottom end (but not really at the bottom end, but very likely your selection would be limited there) and then the "A" trimmer for the near top end antenna tunning (and repeat it few times, as everything influences everything, mainly on these very basic radios).
The most problematic is the IF alignment, there you need the 455kHz reference frequency (you need a fixed point). And that is nearly impossible without instruments.
The thing is, in theory the radio will play at whatever frequency the IF string is tuned to (in the past 250kHz was used mainly in car radios). But the thing (assume you wont hit any alignment limit) is the antenna and oscillator tunning has to track each other across the whole band (so the oscilator minus the IF frequency disctating the received station frequency matches the frequency the antenna is tuned on). And for a given input band range to cover, the electrode shapes (so the C vs Angle characteristic) difference between the two sections of the tunning capacitor have to be exact for the desired IF frequency. And because most common is 455kHz, the capacitors are designed for this. If you use different frequency, the antenna tunning wint track the oscillatior frequency along the whole tuning range.
I will try to replace the electrolytic capacitors, after all they are just four and it will be easy. I also discovered a broken ceramic capacitor between the speaker and the headphone Jack that seems to have the mark "204", which can be the principal problem, so I'll try to replace it before going into the electrolytic ones.
Before the capacitor broke it was damaged so it was working through the parasitic capacitive coupling all that time, hence the low signal.
The ceramic capacitor is just a feedback frequency compensation, so the amplifier remains stable. If it breaks in a way just some part chips out, it wont influence anything. But if it will be missing completely, most often nothing really happens (maybe except when you connect headphones on longer cable), worst case the amplifier may start to oscillate at supersonic frequencies and seem to loose power and get extra distortion.
But in any case better to have it there. Are you sure it is "204" and not something like "201" or so? Because with the one just beside the headphone jack I would expect something like the 200pF (so code "201"). To get the value from the code, you write the first two digits and then add as much zeros as the last digit says to get the value in pF, so "204" would be 200nF (too much for a feedback capacitor, if I identified its connection correctly), "201" would be then 200pF (what I would expect at such place; I would expect something between 100..470pF).
In total Ive seen there 4 ceramic:
1) in the base of the frequency converter (oscillator + mixer) transistor coupling the antenna signal to the base, just beside the antenna holder (you may see the wire to the antenna coil from it) Would expect something around 100pF..10nF.
2) is the oscillator feedback to the emitter of the converter transistor (just below the bundle of wires from the antenna coil), expecting about 4.7..22nF there.
3) detector low pass filter (between the tunning capacitor and volume control pot), expecting something along the 4.7..22nF range
4) Audio amplifier feedback stabilization (just beside the headphone jack), expecting something in the 100..330pF ballpark
By the way I see the lead to the speaker broke as well, make sure you connect it to the correct point (it should go where the jumper wire to the jack goes, aka positive battery terminal).