Welcome to the forums!
It has been in download mode for the past hour with the screen showing "downloading.. do not turn off target". So basically I dont think the download mode is going to work either.
It'll sit in Download mode until the battery dies - the phone is waiting for you to download something to it, either using the Kies software (just Google it - look for v3 if your phone had the 4.3 update) or Odin. If you're not familiar with either of those then you may want to try Kies - it'll handle getting the correct firmware for your phone.
Here's a quick summary of what to do:
- if you don't already have the Kies software installed on your PC, download it (just search Google) and install it. The first time it runs it'll update itself to the latest version so make sure you run it once before proceeding.
- put your phone in Download mode: with the phone completely off, press and hold the Volume Down and Home and Power buttons simultaneously, and release them all when you see the Samsung splash screen
- connect the phone to your PC with the USB cable that came with the phone
-- if you've never had the phone connected to your Windows-based computer before, you'll see messages about installing drivers, etc - just wait until this is done (may take 5 or 10 minutes) [I don't know what happens if you have a Mac - it probably just works]
- in the Kies software, select the second item in the Tools menu and just follow the prompts to enter the model number (in CAPS) and IMEI/Serial Number (both found under the battery - it's ok to remove the battery at this point)
- the Kies software should start downloading the correct firmware for your phone from the Internet; once that's done (depending on your Internet connection speed) it'll begin downloading that to the phone (this probably takes 10 minutes or so)
Edit: if there's a Best Buy near you then take the phone in and ask them to reload it for you.
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