Can it be? Possibly (depending on which part is dead). Can it be done for a reasonable price? That depends on the value of the data you're trying to recover. The starting price for a job like that is in the hundreds of dollars. (A working motherboard has to have its storage chip removed and replaced with the one from your bad motherboard. If the chip is still good, you can recover the data just by backing it up normally. Working at the chip level isn't something every shop has a tech who's capable of doing.) Of course, if the storage chip itself is bad, there's nothing to recover - it's gone.
That's why backups were invented.