I have a 13 inch Funai VCR/TV combo. The power won't stay on for more than 10 seconds and the tape just won't eject. It's an eBay purchase and worked with 2 different tapes.
Many people had the same problem with Funai
Here are some tips for solving this problem:
Perhaps some electrical tape over the little tape sensor stalk, which is roughly between the two reel hubs.
Take a VHS tape apart and removing the tape from the reels and using the empty case to "fool" it into allowing the TV to stay powered up.
The small rotary switch under the transport cam gear gets oxidized and the unit thinks it needs to eject the tape even tho it is already out. Usually they make a loud clicking noise as the worm gear slips on the drive gear. It will eventually break the drive gear or loader gear. Cleaning that switch usually fixes that problem. On some later ones the tension arm won't move properly due to a broken pin on it's lever underneath.
You might need to cover the end of tape sensors. They are so out in the open on many models that you have to cover them to avoid problems when running it with the back off.
The LED down under the prism opens and shuts the set down also. Remove the prism and use a cell phone camera to look at the LED. It can see the infrared. If the diode is dim or out, use one from an old remote. Cell phone cameras work to test remotes also.
You may have damaged gears. You can get information on fixing it here www.fixya.com/
I found a solution to a similar problem: www.justanswer.com/
When funai VCR dvd player was turned on it didn't want to stay on.
This problem was solved as follows:
1. Remove the power to the player, unplug it from the power socket.
2. Wait 10 minutes.
3. Connect the power again to the player and turn it on.