Hurray! It’s working again! 
Big thank you goes to tormod for his help.
Here are updated steps:
- Dismantle DSO
- Find CN7 connector
- Short-circuit the PIN1 and PIN2
- Connect PIN4=RX, PIN5=TX, PIN6=GND (try to swap RX and TX, depends on USB cable, I had to do that with mine)
- Connect the battery and turn it on
- Download and install Flash Loader Demo
- Run Flash Loader Demo, select correct COM port, press Next, then I selected ‘512 mem version’ (can’t remember exact words) and also 0x80000000 from pages list
- Select your DFU file and download it to your device
- All done, now you can update everything else normally through ‘usb’ upgrade mode, FPGA, SYS, APP
Only problem I have now is that I bought it with:
Hardware Ver 2.81
DS203 Mini DSO SYS Ver 1.62
DS203 Mini DSO APP (PLUS A1) Ver 1.13
…but there’s not DFU file yet for my HW version at wiki pages. Wiki says that for “Hardware V2.81 - New FPGA chip is used, so FPGA configuration file has changed. SYS and APP are still compatible with HW2.7x version”, so I believe everything will work fine, except it says HW 2.72 on initial screen. After I downloaded DFU for 2.72, I upgraded FPGS, SYS and also APP to versions I bought it with.
BTW, trick with getting license key didn’t work. I tried DFU and SYS from this thread, but it didn’t work. Anyway, to confirm license key on the load screen is no problem for me.
Thanks again. Hope it helps also to someone else. If anyone gets bored, get DFU for HW2.81 please