How do I check if it is alternater or battery

you've had the misfortune of getting a bad rebuilt alternator-sorry-they should give you another one -I hope its not hard to replace-Denny

First off the gas thing might just be coincedence, second sounds like an alternator problem to me. Try this make sure you do not leave any lights or doors open for the battery to drain at night, Make sure your battery terminals are clean and tight, then to test to see of it is the alternator start the engine and with it running disconnect the battery terminals. I can not remember if it is the positive or the negative terminal to disconnect, so carefully start with the positive then the negative terminal and disconnect them from the battery. Be sure to not let the terminals touch any metal while one side is still connected to the battery. If the alternater is bad the car runs only on the charge of the battery, so once the terminals are disconnected from the battery the car will die. If it stays running then the alternator is good. Then I would look at the starter, TO be honest the only way I can truly diagnose the problem is to see for my self. To see if there are any noises, signs of other issues, Or clues that would help rule out the number of possibilietes.
Hope this helps

try and jump start it

first you half to determine if the alternater is working. you do his by jumping the car and while its running take of the neg cable off to the car if it dies then you know the alternater is not working properly,
if it stays running you know you have a electricalen short you half to trace down

sounds like alternater is not charging-however you should charge the battery and have it tested-if the battery is getting weak it can cause the alternater to over work causing a failure

your alternater could be bad and not charging the battery, get it cranked then remove a battery cable. If it stays running, alternater is good if it dies alternater is bad

sounds like your alternater is not fixed. Your car ran off of battery power till you drained it. Complete alternater repair and charge battery. You can check if your alternater works by starting car and disconnect positive cable if it stays running your alternate is fixed. Shut car off and replace positive cable.

if you have a multi meter disconnect positve battery terminal and put red wire to battery and black to battery cable put multi meter on resistance should be 0.005 or less if more then check for things that may be plugged in to cig lighter etc turn door lights off etc dont turn key on any more than 0.005 will drain battery

Could be battery. The starter takes a lot more amps than the lights or radio. You should get a jump to start the truck. Then drive to your nearest chain auto parts store. Most of them will do free battery and charging system checks. You could also try disconnecting the positve ( red) terminal of the battery after you get it running. If the engine dies your alternantor is bad. You should also get your battery checked if your alterator is bad. Sometimes a bad alternator damages the battery.

Ok, i understand that you have replaced the alternator, but there seems to be a non charge state in this case. i recommend checking the charging system. use the procedure below to isolate this issue.

Wear protective eye wear and clothing and remove all jewelry when checking your battery and charging system. Jewelry is a good conductor of electricity and is not recommended. Most batteries wear out every 3 to 5 years and need to be replaced. Always replace your battery with an equal replacement battery to assure proper operation. Automotive batteries have a +positive terminal (red), - negative terminal (black). The battery in this illustration has a protective cover over the positive terminal to prevent short circuit in case of an accident. Electricity is stored in the battery and then supplied to the vehicle when the engine is not running. While the engine is running the vehicles alternator charges the battery for future use. (Note: never disconnect the battery while the engine is running. If the battery cable is disconnected from the battery a spark can be generated which can cause the battery to explode or a major electrical malfunction to occur.)

To check a battery surface voltage, remove the positive terminal protective cover. Connect the +positive side meter lead (red) to the positive side battery terminal. Connect the - negative (black) side meter lead to the negative battery terminal. With the vehicle not running and the car sitting over night the battery voltage should be between 12.5 and 12.8 volts.(You will need to use a voltmeter for this testing procedure)

The alternator is rotated by a drive belt driven by the vehicles engine while it is running. Electrical voltage and amperage are generated to recharge the battery and supply voltage to the electrical system of the car. The alternator is held in place with mounting bolts. There is a main electrical wire on the rear of the alternator that supplies voltage to a main voltage junction box. If your alternator is not charging properly, your battery will slowly drain down from operating all the electrical systems in your car and stop the car from running.(most non charge states will be the cause of a loose belt or a low tension rate, due to a mis-adjusted alternator. make sure you have enough tension in the belt for full rotation of the alt pulley)

Next, you will need to check the alternators output with the Amp meter.

Testing the amperage output of the alternator is good for measuring the amount (not the level) of voltage the alternator can produce. This test can be tricky because if the alternator is weak it can still show it as producing amperage. Which is good, but if the voltage is low, it will still allow the battery to go dead. To check the amperage output of an alternator an amp meter is needed. Once the meter is connected start the engine. Next turn on all electrical accessories and raise the engine idle to about 1200 RPM. The alternator should output the max amperage it was designed to produce. Example: a 90 amp alternator should output about 88 amps. Note: An alternator cannot sustain maximum output for long periods of time. If the alternator is forced to operate at maximum output it will overheat and fail. An alternator is designed to operate at max amperage output only for a reasonable amount of time.

((Connect the voltage meter lead the same way you would in a battery static voltage check, Start engine (do not drive) at engine idle the voltage should be between 13.6 to 14.3 volts. If not the alternator may need replacing.)))