Unfortunately if it's getting power but not responding there is little that you can realistically do. When you state "Power is connected ok" I presume that this means you have already tried using the gumstick rechargeable battery (which doesn't last forever, BTW), and also the charging stand. If you have tried both of these, then it's clearly not an obvious fault such as a broken power input socket. You can also try connecting the optional external dry battery case, but this was an optional item with the N-710 and rarely purchased by users, or you can try disconnecting the ac adaptor from the charging stand and connecting it directly via the socket on the player marked DC IN 3v.
The fault is likely a really simple one but the MZ-N710 and almost all other portable MD players were never designed to be repaired and consequently are really difficult to dismantle without causing more damage. When I used to sell these products I was told by the Sony servicing centre that for all but the most minor issues warranty claims were dealt with by destroying the returned unit and sending the customer a complete replacement.
Spare parts were not commonplace when the units were a current model, and now they're as common as freshly laid dodo eggs. Your only realistic fix is to replace the unit.
This may sound negative, but it's not: because MD is now an obsolete format there are millions of perfectly good units lying unused by those who have upgraded. Except for the later and far rarer HiMD models and also flagship regular units like the MZ-N910, almost everything else is near worthless so folks tend not to bother with selling them. As a result it's quite easy to pick up MD equipment for free via your local FreeCycle and Freegle groups; apart from my own MZ-N910 (still in regular use and has a far superior sound quality to any iPod) every piece of MD gear I own was obtained for free, usually with loads of minidiscs as well. Don't be too choosy about what you may be offered as most of the Sony NET MD players (any MZ-N model) can be easily hacked to give them most of the features of the flagship MZ-N910
If you do end up recycling your MZ-N710, then keep all of the accessories as they can be used on other players which you might acquire.
I hope that my answer has been of use even if you cannot fix your player. Please take a moment to rate my answer.