I Have a Sony Z7. The tape door doesn't close and the tape doesn't slip into place. How to fix that?

It needs servicing at a Sony Service Centre. You can't fix electronics and servos at home unless you have equipment. There is a video here, because it in a known issue.

CAMCORDER TAPE DOOR WON'T CLOSE { C:32:11 } FIX ...

? 13:13
https://www.youtube.com/watch?v=CBqP-Q86UyM
Jul 9, 2014 - Uploaded by GotNoEvidence
Here is a fix that does not involve disassembling your camcorder, sending to the ... This worked for us when the tape door wouldn't close on our old Sony HDR-HC9. .... is you can use the same method to REMOVE a tape when the tray will not lift! ... Yes yourvideo helped me fix my DCR-HC96 camera.

Sony HDR-HC3 Tape Door Won't Close with C:32

Sony Handycam CCD-TRV58 Hi-8 Analog Camcorder
1. Per the manual on esupport.sony.com
- if the power is disconnected door won't open, and if the battery is the dead the door won't open.
Plug it in and hopefully you can get the tape out.

Did this work?

Nobody answered this? Well that's disappointing. I have the exact same problem now at the end of 2018 six and a half years later. Searching on.

big problem with sony as you can see im a pro tech but had the same fault with mine. and it broke my heart 4 weeks old and sony dont give a dam ironicly a mate told me slam my fist under the bottom and it will close after hrs of trying to fix it i took his stupid advice and after many hits it closed and worked great for a few weeks

The film doors in most 35mm SLR's is spring loaded with a release from the rewind knob. Chances are your spring has lost tension, slipped out of place, or the teeth that grab the door have been damaged. You can always use the handyman's secret weapon (duct tape) to fix the problem, but if you're looking for a more permanent and less gooey and unattractive solution you're going to need to find a shop.

If there aren't any locally, you can find some online, or google KEH Camera if you're not sure who online is reputable. It'll run you $35 for a repair estimate which is waived if you decide to have the work done. Keep in mind some parts, for some cameras, are hard or impossible to come by so your model may or may not be able to be repaired, or may be priced outside of what you're willing to pay to have repaired.

The lower hinge on each door may have a door closing cam. It raises the door up ¼ inch when opening and this assist in closing the door. If it's wore out and doesn't work the door may not seal and the gasket can be damaged. Watch the operation of the door to see if it rises up when opened.

Leave the door shut and let the magnetic gasket hold the door in place. Put something between the bottom of the door and the floor to hold it in case it slips.
Remove the bracket holding the pin and hinge assembly taking note of order of removal of parts. Slide new cams on. You probably need two.

Many times it's a belt slipping. Since the tape isn't pulled into position, it's rewound and the tape ejected. A damaged or mal-adjusted switch could cause this too. The most you can do is blow it out with compressed air to see if that helps. I doubt there are many thing the end user could do.

mechanism is faulty.flex cable (FP-031-12) is broken. replace complete mechanism or flex cable (FP-031-12) by any service person

Common problem with this mechanism. In order to fix the problem you will have to replace part called CHASSIS LS. Expensive repair, probably not worth the effort.