Can anyone help with a very weird starting issue on a 1998 Mercury mountaineer V8 5.0?

[Boston City Lifestyle]

OK i had an issue with my alternator going bad and my lights started to dim out one day but i made it home the truck stayed running(lucky for me)but it wouldn't re-start as soon as i parked it when i got home. I knew it was alternator very obvious so I picked up a new battery and a OEM alternator installed them and the truck started right up and lights came back to life and the battery level gauge was right where it was suppose to be. Now something funny started to happen right after i installed everything a few hours later. Sometimes not all the times the truck would not start up but the starter is turning over full power it sounded like it wasn't getting gas. Now the funny part after this would happen i would let it sit without trying to re start for a few minutes try it again and it starts up. Once it starts it stays running no problem and doesn't stall out or anything it's all normal. I'm assuming because of this it's not the fuel pump or the fuel filter because it would stall out while driving right but it doesn't it runs fine after it starts up. It does this starting thingy when it feels like it but no one in my family wants to drive thinking it will leave them stranded. Like i said if doesn't start up when i try to start it i let it sit for a little and it will eventually start up and stay running very weird? It happened right i did the battery and alternator install but the install is correct it was very easy to do. It never did this before started up fine all the time so what could be wrong can anyone pin point me to what to do or check thanks?


It has a 144,000 miles on it
After the first failure i turn the key back and it's in the off position so the fuel pump is not running. I was thinking this to by leaving the key in the ON position for a couple minutes and then start it but i was thinking it would flood it out.But no the key is not in the ON position so what you think now.