|One long beep - bad or improperly seated RAM modules. |
Proceed as follows:
Switch off PC and switch off PSU rocker-switch if it has one.
If no rocker-switch on PSU, disconnect power cable instead.
Discharge static from your body by touching bare steel on computer chassis.
Carefully remove and reseat all RAM modules.
Replace power cable and power up.
If still no joy, one or more RAM modules need replacing with new ones.
Suggest you use the Crucial website with a working PC, select the model of your Gateway and they will show what they have in stock that's compatible:
Edit: new PSU should be fine as long as it's wattage output is at least as high as the old one, though higher would have been preferrable.