sounds to me like the directional contactors are worn out, dirty tips maybe
put tip kit in them or replace contactors

but by all means DO run the accelerator test in onboard diagnostics to verify that all the steps in the accelerator are working correctly.

pull the drive fuse
turn on key
put run/diag switch on card into diag mode
it will show d on display
then cycle switch to run test, each test you have to do in order it looks for so u need diagnostic sheet to tell you which one is which when it asks.
there should be a schematic under hood showing you panel diagram and will also have diagnostic routine on this, if it's gone then you need to get the manual.

as you run each test it will advance to next test if it passes.

keep cycling till it get to accelerator test and if it pass then accelerator is ok.
i'll look and see if i have this diagram and may can send it to you to help you if you need it now.

put your email in your profile in signature and enable 'show signature' when you post to thread.

Thank you for the tip, ill try that..
I really appreciate all of your guys' help.

Google Cat F35 manual and you should see some for sale on Ebay. The only other way is contact your local Cat dealer and see if they have one that they would be willing to make a copy for you.

Thanks for help. I do wish I could locate a service manual but have had no luck. I have replaced the accel control box with a supposed working unit. It didn't change anything. Here's what I did find. There is a set of dual contactors connected to capacitor. It does not always engage. But when it does truck takes off and seems to operate properly with the accelerator pedal pressed either partially of fully. Then it seems like it dies out after a few seconds. Have no idea hat should activate that set of contactors. Thanks again for any and all help

there is no need to type in caps, that is usually consider "shouting".
In this truck, it is possible to use the "on-board diagnostics" to be able to check the 'steps" in the accelerator control to check to see it is working correctly.
my quick wag is that your accelerator control box has lost a c-clip on the part that moves inside to block the operation of the photoelectric sensors.
you should get new or known good accel control box to check or get the manual and use the onboard diagnostics.

NOBODY HUH! ANY OF THE EXPERTS HAVE ANYTHING AT ALL, ANY SUGGESTIONS???