Another "start" problem

[k9byrd]

It's a 97 Suburban (GMC) that won't start in the morning. I have not found this problem reported in the forum, so I hope you can give me some ideas.
If the sub sits for a couple of days, it won't start. No cranking. No clicking. The battery is brand new. If I fully recharge the battery, it starts like a charm. Sometimes (not always) this will happen after a one-night stop.
Here is something I noticed. Sometimes when I hold the ignition key in the start position for several seconds (and press the gas pedal once) the engine will start. Today, it was dead. I need to re-charge the battery.
Should I replace the starter? And if something is discharging it overnight, how do I trace the problem?
Thanks, John

[feac]

Here are four things to think about.
1. Battery discharged or low
2. Fuel not reaching the fuel injectors. Check the fuel lines, fuel filter and fuel pump.
3. problem with the fuel injection system
4. Defective spark plugs
Thank you
Adam Forsythe

[k9byrd]

Thank you Adam (feac) for your suggestions. I finally got the problem resolved. It was the starter.
John