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That suggests that circuitry, at a guess either the power supply or more likely the control board or central circuitry module, is subject to a common failure of aging electronic equipment: it is becoming heat-sensitive, and as it does so, a component in it will be off-specification or not-functional until it is thoroughly warmed up.
This is especially likely, if you have noticed that the problem takes longer to get through progressively as time goes on.
If that's not possible, if the problem just suddenly set in, and if it doesn't start up fast when you shut it Off briefly after operating it for a time, then within half a minute to a minute or two, you turn it On again, and it works at once that way (when thoroughly warmed up, that is), then something else is wrong, but again, probably with the central control circuitry module.
If you were thinking of repairing it yourself, the obvious way to do so (given that the Roland facility thought the same way I do, and that part is no longer available from Roland) is to obtain a failed FR7 of the same model, and get (hopefully) a board or module in working order out of it. Look for such failed and for-sale (at a reduced price for sure!) FR7s by searching craigslist.com for your region, every 5 days or every week... or by checking freecycle.org. (On craigslist, consider both the For Sale section, and the Free section, of course.)