If that's one long and two short beeps, it means there's a video error, and the BIOS cannot initialize the video chipset. This indicates a CMOS-ROM and/or system BIOS problem.
Try the following:
1. Replace the CR-2032 CMOS ("BIOS memory") battery. See E - Battery. The tiny clip on the right side of the battery in the graphic must be pushed away from the battery to free it up for removal. The tiny clip may also need to be pushed aside to allow inserting the new battery. Note that the battery goes into the holder with the "+" side up. Wait for at least 15 minutes after removing the original battery (to clear the CMOS-ROM), then insert the new battery, close the case, and boot up.
2. Replace your motherboard. I'd recommend replacing with the exact same board, since that'll avoid having to back up the data on your hard disks - which can be especially nasty with a Gateway machine. Plus, you can use your existing CPU and memory sticks (assuming they're not damaged). The exact same board is available here.
If you aren't familiar with removing and replacing CPU's, you might want to consider having a professional computer person do it. There can be problems getting the CPU off of the original motherboard without damaging the CPU and/or the CPU heat sink and fan assembly.