97 Blazer--Fuel Pump/Relay?? NEED HELP!!

This issue started first when I noticed it took a long time for the fuel pump to stop when the ignition was turned off. Then I started to notice it didn't always sound like the fuel pump was turning on when trying to start (which it didn't start) but eventually the blazer would start. Now, she won't start, don't hear the fuel pump turn on and did I mention that the past 2 weeks at night the headlights would dim a couple times just for a split second. Someone said it may be a relay issue. I checked fuses but all looks good. I found a relay box in the glove box but haven't tried to open it yet. What would I even look for. I am sure some of you guys are smarter on this thing than I am. Thanks for the help

I found a relay box in the glove box but haven't tried to open it yet. What would I even look for. I am sure some of you guys are smarter on this thing than I am. Thanks for the help

Behind that cover you'll find three relays.

They're all the same, so you can swap them out to see if the fuel pump relay is the cause of your problem.
The other relays are for the A/C and the Headlights (I think, not completely sure about the third one).

With your lights dimming, perhaps a bad alternator.
What was your volt meter reading? Is your battery OK?
Does the starter turn the engine over?

Starter does turn over and the battery is only 1 mo old.

Sounds like your battery is down, just because it's only 1-month old doesn't mean it's fully charged. Sometimes a battery will set on the shelf for a year before it's sold. Also, as stated, you could have an alternator problem.

Try jump starting it. If you get it running take it to AutoZone, etc, and have the battery and alternator checked for free.

If jump starting don't work, pull the battery and have it charged and checked.

Once you get it running then you can further check out the fuel pump problem.