Solution:  According to Yaesu: "The technical explanation is that there is some protection built in to avoid pushing the display to full blast from a very cold start which would result in a shorter life span for the display. It appears to be a normal event for a lot of owners, and as long as the display comes on full power eventually, it is probably "normal".
 

Problem: Last week I went on vacation, after my return, when I turned on the radio, for the first time ever the display was blank for a few seconds. Then the radio worked normally.

Solution/Comments: The problem of delayed turn on of the display appears to me to be directly related to how long the radio has been turned off. At times I may not use my MP for a week or more and when I power it up I might have to wait as long as 5 seconds for the display to light up. If only powered down overnight, the display comes on immediately the next morning. It does not seem to be related to whether the antenna is connected to the radio or not because during those extended periods of power off the antenna is connected to a different radio (and not to the MP). I'm not at all concerned about this and just write it off as one of those nuisance things. Earl, K6SE

If the display does not come up at all, see Display Failure

Solution/Comments: I read all the problems with the slow turn on of the digital display on the FT1000MP but until a few weeks ago I never noticed it on mine, but over a period of time the dwell time between pushing the on off switch and turn on became quite noticeable, I was blaming the on/off switch pushing it in and out each time seemed to improve it until the next cold start. then one afternoon while sandbagging on 20m the 1000 shut down completely.

Off came the covers and the fan removed to then check the supply leads from the power supply to the regulator board. I found it read only about 9v, not enough to pull the relay in on the regulator board. so after removing the front panel and taking the power supply out then came the struggle, take the switch mode supply apart, quite a job in itself, then looking around I found the small electrolytic capacitor C38 a small 10mf 50vw had failed! Upon replacing this cap, testing the power supply showed 13volts again, so major rebuild to get it all back and my rig now has a very fast display turn on, comes up almost instantaneously, also the performance seems to be improved too, I suspect that the rig suffered a gradual voltage drop over time and the slow performance fall off wasn't noticed, only the delay in the dial light up

Doug VK6DG