Cadillac Repair: no fuel response, cadillac deville, response question

Question
QUESTION: i own a 1991 cadillac deville 4.9l the car starts fine with no problems and it runs good with no problems at all but after 30-45 minutes of driving then i come to a stop or slow down to less than 15mph or so i then  try to get the speed back up but i have to do it barely pushing on the accelerator if i step on it as normal the car will not respond even if i get it all the way down, the car will keep running (and not turn off) at low speed  not responding to how much gas i want, in other words i have to barely push then realease on the gas pedal repeting the process many times till i get the speed i want. on a hill the car will not get enough power to go over it and the push and realease process will only get me to about 15mph, so i have to park and turn the car off for about 15 minutes  then start right up still having the same problem but i'm able to push on the gas alittle further, in another 5 minutes and another hill and i have to do it again,  if i turn the car off for a few hours it drives good with no problems till the next 30-45 min. or so. i thought about replacing the fuel pump and filter but don't know how this would help if it only does it when the engine is hot.  what do you think the problem could be. sorry for the long question but i'm trying to be very specific.          thank you

ANSWER: When this fault is occurring IS the CHECK ENGINE light on the dash illuminating ?.

Also when this happens look to see if any exhaust parts are glowing RED hot.

You need to check your fuel pressure when this occurs.

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QUESTION: the check engine light is on

ANSWER: Do you know how to retrieve the codes from the computers ?.

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QUESTION: i do not know how to retreive then codes.

Answer
To retrieve CODES:

1. Turn ignition switch to the ON position. Do NOT start the engine.

2. On the climate control panel Simultaneously push and hold the OFF and WARMER (^) buttons for 3 seconds and release them.

3. Codes will start to appear in the fuel data display in a combination of LETTERS & NUMBERS and along with each code will be the word HISTORY or CURRENT.

4. The display will finally stop at .7.0

5. let me know what codes you get and whether they are HISTORY or CURRENT.

6. Turn ignition OFF.