Hi, sorry to dig an old thread. I have the same problem on my DR-40 unit. Mine turns on then shows this screen and shutdown about 5 seconds later. It's in this state for years and I've tried everything. I can even successfully enter test mode, but from there, nothing have any effect.
I'm almost certain this is a problem of a corrupted eeprom (SPI flash). I managed to get a dump of mine with a SPI programmer but then I'm suck. Tascam site have files for 2.50 and 2.51 firmware version, but they're not similar to my eeprom dump. It could be that the firmware is compacted with god knows what algorithm (I've tried lzss, lzma, bz2, etc. etc...).
If anyone can make a eeprom dump of a working unit, I would be very glad. (my unit's flash is MX25L1606EZNI). Thank you.