I have already written a forum post about this oscilloscope, I suspected that the reason for stopping on the start logo was the failure of one of the inverters.
All voltage inverters seem to be working properly.
I was able to connect to the oscilloscope using the PUTTY program and here is what I got in response:
NAND: 512 MiB
U-Boot 2008.10 (Apr 14 2014 - 09:37:23)
OMAP35X-Family-GP rev 2, CPU-OPP2 L3-165MHz
OMAP3 SPQ board + LPDDR/NAND
readenv ERR*** Warning - bad CRC or NAND, using default environment
In: serial
Out: serial
Err: serial
Hit any key to stop autoboot: 0
NAND read: device 0 offset 0x1ff80000, size 0x40000
NAND read from offset 1ff80000 failed -117
262144 bytes read: ERROR
## Executing script at 80800000

Everything points to damaged NAND memory, damaged tin balls under the memory or damaged firmware.
I wrote to the manufacturer about the firmware, I did not get any answer, nor could I find it on the Internet ( it used to be available, but is no longer).
If anyone had a similar problem please guide me to a solution.
I plan to solder out the memory, put new balls on, solder back in and see what happens.
There is a tiny battery on the motherboard ( it had 1.9V instead of 3V), replacing it with a new one did not help.