Onboard computer shows no values + climate does not work

Hello to all, I’ve had the following problem for a long time and it’s been unsolved so far, maybe someone here knows something: The on-board computer of my Mazda 3 (2009) no longer shows the calculations for average consumption and speed etc. as well as the outside temperature. However, the display works. Only strokes instead of the values are displayed. Worse, however, is that the air conditioning does not work anymore. If it is short-circuited, everything works, only in normal working conditions. The on-board computer doesn’t work quite exactly on the day when the “inspection counter” was set to 0, if I remember correctly. I wonder if this could have something to do with the car not knowing the outside temperature anymore? So the failure of the climate is a consequence of the problem with the on-board computer? (Unfortunately technical lay) The Mazda workshops, in which I have been so far, have the problem so far only As described in this way, however, the car wanted to hang on to the analyzer for up to 3 hours, which could result in costs of up to 500 € – that was only too expensive for me for the analysis of a then possibly minor problem. Is there any way to find this problem with your own analyzer and app (forscan etc.)? At Mazda it seems to be quite difficult to find a suitable device… Do you have any other idea? Maybe a cable, a fuse (with which I have already done this before). z check, but who knows) or the temperature sensor (but wouldn’t explain the failure of the BC)? Does your experience tell you that it may be related or rather excludes it? Thank you for every advice, I’m really desperate and my trust in the workshops, which partly wanted to replace the working compressor (1000€ upwards) is severely damaged. Best regards!