I am replacing the hard drive in my gateway 5220

You cannot use a SATA (serial ATA HDD in this machine. You need a PATA (parallel ATA) HDD, also known as IDE, ULTRA IDE, ULTRA ATA. This has a 40-pin ribbon connector & a 4-pin power connector.
Sizes generally available would be 80GB up to 250GB, although very few PATA drives are now sold since SATA is the new standard.

The motherboard BIOS most likely have a hard drive size limit. Yes you can create two or mare partitions to use the rest of the hard drive space.
Go to Control Panel - Administrator Tools - Disk Manager to create a partition and format this partition.

The correct power adapter for the SimpleTech 250GB USB 2.0 7200RPM drive is 12V, 2A tip positive.

sounds like your system is booting up and running due to the hold power shutdown procedure. you might try replacing the video card or adding one if your video is integrated.

Better get a SATA adapter card, as this mobo uses IDE (PATA) harddrives. http://www.legendmicro.com/store/4761_ECS-C51PVGM-GB--Gateway-4006136R-SK-AM2-2000FSB-DDR2-MBTX-AVL---New-C51PVGMGB.lmsp

ok get a windows 7 disk and turn of the computer and ad the hard drive switch on the computer and set it to boot from disk (seems windows is broken on the 500gb hdd) then boot from disk and install windows 7 to the 500 gb hard drive and set in the bios the boot select for the hard drive (if you use win xp more then make that boot primary) then go threw all the rigmarol of installing windows 7 to the 500 gb one and your done it will have bootable hard drives and will offer a choice when first switched on

You can open manually using small metal stick (metal paper clip).
Turn off PC, poke small hole (under the tray) gently. Check the rubber ring (like fan belt that goes to electrical motor), it might too loose.

The GT5220 uses an NVIDIA GeForce 6150 AM2 uBTX 1394 motherboard (part # 40006136R) The only one I could find was a refurbished one:
http://www.partstore.com/Part/Gateway/Gateway/4006136R/Refurbished.aspx?s=google&CID=g8Account78PartNumbersOct08068Gateway8Product

Here's one on ebay:
http://cgi.ebay.com/4006136R-C51PVGM-GB-Motherboard-Repair_W0QQitemZ330401044956QQcmdZViewItemQQptZDesktop_PCs?hash=item4ced6fd9dc

if u have new harddrive then simply first remove crash harddrive from computer .
Then if u have sat harddisk connect it with sat cable .
I fu have ide harddisk tehn connect with ide data cable. simply.

Since you do see the logo I concur with the bad hard drive assessment. If you have data that you need to recover from your existing hard drive don't throw the drive away. You can almost always get the data back but it may be expensive.

When you buy your new hard drive, get an IDE interface, not an SATA. Your computer originally came with a 250 GB PATA (another way of saying IDE).

You'll also need reinstalltion disks for Windows and any other programs you want on your computer, especially the Gateway drivers. You can find those here.