I had do three experiment :
1. I use internal timer for controling the LED on and off, when I select 1MHz, 8MHz and 16MHz, the interval between LED on and off is different, so cpu speed is correct as I select.
2. I set cpu speed to 8MHz, plug USB 5V as power source, and load a sketch for lighting LED on and off.
After 5 seconds booting, Digispark start working and light the LED, then I attached the CR2025 and unplug the USB, the power voltage is change from 5V to 3V, but LED is still working and good behavior(but light from LED is getting dim).
If I use CR2025's 3V to boot Digisparl, it is almost fail, LED is not working fine.
3. I use multimeter to measure current , in first 5 seconds it cost 12~15mA.
When sketch is load and LED is lighting, it cost 7~8mA.
I guess in the first 5 seconds, the time bootloader micronucleus wait for sketch uploading, cpu speed is 16MHz.
After 5 seconds, sketch is working, and cpu speed is turn to what you select.
In my case cpu speed is down to 8MHz.
Maybe it can explain why my CR2025 is hard to boot Digispark and work:
3V is not enough for 16MHz.