Recover old Li-on battery

I got a mobile phone with what seems to be a dead battery:

• the phone would not power on
• the battery was approximately at 2.4 V
• so sign of charging after plugging into USB charger. The battery might have reached disrargelevel that is below acceptable level so phone would not regognize it as safe to operate (charge)

I used my new imax b6 charger at first but it showed a broken connection.
On the second measurement battery voltage was 0. So I suspect imax B6 caused some internal battery locking.

HTC Desire C

Next step was to try to supply a power source to check and identify if the phone still operational. I used step-down module (see on the picture)  with adjustable V and A values.
On the first attempt (approximately 4V and 0.1 amps ) to power it on I got a short blue blink from step-down module. I looked like 0.1 is not enough to boot up. So I have increased to current to 1 amp and phone successfuly boot up.
Next I tried to improvise and contstruct battery dock to try to charge the battery. It did not well and as a last resort I used phone itself as battery holder. I used original power pins to supply power to the battery and the phone itself. For that I used simple power connectors like in th image below:

 I bent pins to resemble hooks and attached them to power pins:

In the image above you can see that battery is being charged (blue led is on). After about 30 min I got around 5 % of charge and was able to power phone on it's own.