Is PREL 13.1 the Problem, or is it the burner in my computer?

Question

Once again, I am hoping the expertise of the devoted leaders of our USERS FORUM can solve my problems.  Thank you again for your devotion and efforts on behalf of all of us who struggle to produce our masterpieces.
I purchased Pre El 13 on Dec 29 and installed it 1-5-15.
    My computer—Hpe 580t, Win 7 Professional 64-bit OS with a second internal 1 TB hard drive;     Burner Drive F: Name--    hp CDDVDW TS-H653T
           Intel R Core, TM i7 CPU 950 @ 3.07 GHz,      RAM 9.00GB 
I use a Nikon Coolpix 100 camera to video indoor pickleball tournaments at 5 mega pixel size. These video clips range from seven seconds to one or two minutes.  I use PREL 13 to arrange the clips into whole games, which requires a lot of editing to eliminate in-between rallies and to correct lighting.  Starting with as many as 5 or 6 hours of clips, I pare down to a movie that will fit comfortably on one DVD—less than four GB, or 1 hour 45 minutes, of finished material.  After struggling alone for three months, I was able to produce such a DVD within about two weeks, thanks to A T Romano.
THE PROBLEM—after all the time and effort to produce a good movie, Prel won’t recognize the burner on my computer; therefore, I can’t produce a DVD disk.  (I always go through the Publish and Share dialog for burning a DVD with recommended settings.)  See Figure 1—below.
    Even after I click on RESCAN several times, and make sure a blank disk is in the F: burner drive, PREL 13.1 refuses to find the computer burner.
    Due to insufficient Upload speed (usually between 2.5 to 3.5 mbps) internet speed, sharing my Videos is wholly dependent on burning one to two hours of edited videos to DVD medium.  I have tried saving the movie to a Video_TS file on my computer, but cannot save all the components of the movie in the same TS file and be able to burn a DVD using ImgBurn.  The menus and scene markers are missing completely, and some of the video clips are also missing.  See Figure 2.
    I want to use the Movie Menu Tools and scene markers to designate the beginning and ending of each scene, which I will burn to a DVD for playback on TV.  Movie menus and scene markers only work if I use the burner through PREL 13.  Other outside burners, like Windows Movie Maker or ImgBurn do not recognize the movie theme or the scene markers, nor do they provide any way to skip to a certain scene marker on the disk.
   While working on other projects, I was able to burn DVD’s; however, I have become increasingly frustrated, because the vacant box indicating no burner detected is now happening every time.
    Would this problem be solved by upgrading or installing another burner?
    Or is this some ingrained bug in the PREL 13 software? (Such as; a burn can fail by inserting a stop marker at the end of a movie or scene)
Another PROBLEM—there is no way to save the edited video clips to a file, to be used again when PREL refuses to recognize my computer’s burner, which requires me to start all over with the editing process.
    To avoid importing all the raw videos to PREL in an endless chain of clips and editing, I tried saving each game, or sometimes a whole match, to an mpg2 file on the computer.  Then it could be returned to my project by dragging and dropping the file onto the timeline in the proper sequence.  This method works in theory, but again, PREL won’t detect my burner in PUBLISH AND SHARE.
Thank you so much for sharing your knowledge and experience with me. 
Sandgrass
Figure 1
Figure 2

Answer 1

The complete message is missing--again.  I'll try posting directly into this frame.  Sandgrass.
ATR—my answers to your Q’s and instructions are in red (except where indicated by ANSWER) below your statements..  It got sort of hairy trying to carry out all these steps and tasks below.
Sandgrass
Thanks for the great post full of information.
For troubleshooting purposes, make one or more copies of your project - File Menu/Save A Copy - and work from copies each, each with a different name than the original.
Did you look at the burn to disc or folder with and without the Intel HD Graphics 2000 or Higher disabled?
    ANSWER-- Please see Edit Menu/Preferences/General.-----------  I unchecked the box for acceleration and  - - - See LOVELY Screen Shot (Fig 5) Burn Status = Ready. 
How do you know all this stuff?  I’m afraid to touch boxes and choices for fear it will really mess me up, and unless someone instructs me to do so.
Is the burner recognized and can you burn to disc if you remove the Timeline menu markers and Movie Menu from the project?------------Burn Status shows Ready!
With no Menu Markers or Movie Menu, I tried a Burn command after rechecking the Hdw Accel. box, and the Burn Status shows Ready with the box either checked or unchecked.  Since the Hardware Acceleration checkbox seems to be related to my problem, (Fig 6) is a Screen Shot of my computer’s two Drivers, F: & G: .  Is Hardware Accel necessary for good quality movies such as I want to produce? 
A. Could this one box be the source of all my troubles?
B. Why is it now working either way?
3. The 15 minute duration limit is for Instant Movie. You are not using Instant Movie so, with your19 minute Timeline, you should have no 15 minute restriction and should be fine in that regard. One thing you could check out about your Timeline structure - see if it makes a difference in any of the workflow - look to the Timeline spot about 00;17;05;02 - what is that clip and can you fill in the empty audio space under it with muted audio?  Clip at 17;05:02 looks normal to me.  There is a gap in the audio at 17:20:21 where I inserted  a Black Video and Title. Muted audio?  Couldn’t find a reference to Muted Audio.  Sorry.
4. Let us go back to focus on the VIDEO_TS Folder from the saved burn to folder route....
Publish+Share  -- Disc – DVD -- burn to: Folder (4.7 GB)...
In the Quality area of the burn dialog, what is displayed for Space Required and Bitrate with and without a check mark next to "Fit Content to Available Space"?  
(Fig 7) is a Scn Shot of the Settings for saving an MPEG file to computer.  I don’t know enough to mess with most of the presets when the window opens.  I did bump up the Quality to high 80’s, low 90’s.  The Field Order is preset to Lower First.
Are you taking only the VIDEO_TS Folder in the saved Premiere Elements folder into ImgBurn?
ImgBurn
Write Files/folders to disc
File Menu/Browse to source folder (that being only your VIDEO_TS Folder)
  Here we go!  I was opening the TS folder and trying to choose what files had to be imported to ImgBurn!  OK—so you take the entire VIDEO_TS Folder to ImgBurn? 
    Out of time for today.  I will proceed from here and report back to you, hopefully tomorrow.
(ANSWER CONTINUES, SHOULD BE IN RED.)
Since I will be pushing the limits of a 4.7 GB, two-hour movie for my third project, how long should the ideal segments be before saving to an mpeg folder, to be dragged and dropped back to my timeline if I burn  straight to DVD?
Which way would net the best DVD quality—Burn straight to DVD, or save to a VIDEO_TS Folder and use ImgBurn for the DVD?
You deserve a medal for all you have done for me.  Thanks so much, ATR         Sandgrass
Let us review the above and then focus in on what next.
ATR