First try programming the Digispark - then unplugging from the computer and running it from some other 5v (5v pin or usb connector) or 7v-12v (Vin pin) power source - the issue might be if you have it plugged in the computer still, the USB communication is interfering.
Some do light very dimly when they shouldn't, this is a result of the Charlieplexing and the chip being used - but the one not turning on is unexpected. Since you've tried a second LED already I'd look if anything was being shorted from soldering, etc. The boards are 100% tested so it shouldn't be a faulty board.
Let me know if any of that helps,
Thanks,
Erik