VCR tape comes back after insertion?
 

When I insert the tape it comes back out within a few seconds most all the time. When it does stay in and I playback there is a horizontal white streak sometimes in the middle of the picture even after I cleaned the heads with a cleaning tape.

Have you tried opening the case? I ask because I just fixed a cheap old Emerson player that had a very similar issue. When I opened the case there was very obviously a piece out of alignment and it was easy to pop back in line. I have no experience with this tech but you may get lucky and see the issue visually such as with mine where there was a physical obstruction to the mechanism's proper movement. Just a thought...

what make and model is the deck?
cleaning tapes do nothing but smear dirt around.
you need to take the cover off and do a manual cleaning with chamois and alcohol.
open the flap and see if the tape creased- if so you will never get rid of the line.

Tape is not folded. The deck is the Sony SL-HF900
1 out of 30 times the tape cassette stays in and I can press Play and it works fine. Most often the cassette
ejects after 3-5 seconds after insertion.

When I insert the tape it comes back out within a few seconds most all the time. When it does stay in and I playback there is a horizontal white streak sometimes in the middle of the picture even after I cleaned the heads with a cleaning tape. [This is a Sony SL-HF900 Betamax]

that model is a Super-Betamax
Betas are wicked cuckoo clocks and a super PITA to fix
i would recommend sending to Mr.Betamax
the 900 is a decent Beta and probably worth fixing

Yep, I agree.
Here's the site: http://www.mrbetamax.com

No video is a common sign of a dirty "ACE" head. This is the fixed head that reads the control track and linear audio. Another issue with these are leaking surface mount capacitors on the capstan motor assembly. If the capstan isn't turning, the deck shuts down to prevent tape damage. There are other possible issues, so it likely needs to see a pro.