I have exactly the same TS50 problem!
I've been using the TS50S for a couple of years, and the exact problem described by VE3UG just developed a few weeks ago - at first intermittently, now every time I power it up from a cold start. The delay before normal reception varies depending on band and mode, but it takes a maximum of 30-45 seconds before settling down to otherwise normal operation. It doesn't seem to happen (or at least not for as long) if it's been powered down for less than a few minutes, so warmup is somehow involved.
If the audio volume is at or above normal level, there's also often a loud feedback-type squeal that only disappears when the volume is turned all the way down or after normal operation resumes. The squeal occurs with or without headphones. Keying the transmitter cuts off the squeal and switches the s-meter to apparently normal transmit operation in all modes. Receive still does not work until after the noted delay.
This isn't a serious problem for my normal operation, but it seems to be progressing - i.e. it's becoming more consistent and the delay time seems to be slowly increasing. I assume that whatever is causing the problem - a dc-dc converter sounds like a likely candidate - will probably fail sooner rather than later and may damage other components.
I'm hesitant to reset the processor unless it's likely to fix the problem - which it didn't do for VE3UG. I can change the battery, but I don't understand how that might help the problem.
I look forward to additions to this thread, hopefully some with specific solutions for the problem.
Aloha from Kona,
AH6KW