I can not unlock my screen and I'm not getting a Goggle prompt or a prompt "forgot pattern?" to respond to.

To find this feature, first enter an incorrect pattern or PIN five times at the lock screen. You'll see a "Forgot pattern," "forgot PIN," or "forgot password" button appear. Tap it. You'll be prompted to enter the username and password of the Google account associated with your Android device.
https://www.howtogeek.com/226942/what-to-do-if-you-forget-your-android-phone's-pin-pattern-or-password/

After pressing OK or waiting the 30 seconds, press navigation key to bring up screen again. I'm guessing you have a Motorola phone, but maybe not. You will get back to the security lock screen but there will be a button on bottom right that states Forgot pattern (or passcode). If you forgot your screen unlock pattern or passcode, tap Forgot pattern (or passcode). You will be prompted to sign in using the Google account you programmed into the handset during initial start up. If successful, you will move to next screen to create a new security lock. You can cancel out of that step and return to homescreen.

first remove sim card and memory card then insert battery and press power button and volume simultaneously. this will bring you to the factory reset. press volume down to scroll up and down and press volume up to select.

I forgot my gt s5300 pattern and forgot my Google Account,how can i open it again?

1. On the unlock screen, attempt to enter your unlock pattern five times.
2. When prompted to wait for 30 seconds, tap OK.
3. If the display goes off, press the POWER button to turn the display back on and then press the bar on the lock screen and slide your finger down to unlock the screen.
4. Tap the Forgot Pattern button in the lower right corner when it appears.
5. Enter your Google Account name and password, and then tap Sign in.

You are then prompted to create a new screen unlock pattern. If you no longer want to use a screen unlock pattern to secure your phone, tap Cancel.

If you forgot you screen unlock pattern then you need to reset it. The simple procedure is mentioned below -

1. Continue to enter the unlock pattern five times until you are prompted with forgot password (forgot pattern in some handsets) at the bottom right side of the screen.
2. Tap on the Forgot Password option and you would be prompted to sign in with the existing Google or Gmail account information. You need to provide the ID when you first register or activated your phone. If you have that, it would be easy to get in for you and then change the unlock pattern (atleast by now you would be remembering your unlock pattern).
3. If you don't know the Gmail ID or the password is wrong then there is only one solution to hard reset your handset. The data present on the added SD card will not be wiped out but you would lose your personal data or information or contacts stored on your phone memory.
4. The procedure for hard reset is mentioned clearly at reset the mobile.
1. F150 Parts.
2. 
   

The factory reset removed the Google account data from your phone. When first setting up a phone, you pair the phone with a google account. On the off chance that was not the first thing you did after the factory reset, you may have to hard reset it again and then go through setup immediately to pair a Google account with the phone. If you have not paired the Google account with the phone during setup, you will not have Google access. If the setup offers a restore from backup (and you did have backup enabled previously), you can give that a go. It would restore settings.

But before you do that, you could try the following. I don't think they will work for you but the powers that be might smile upon you.

Try entering your user account name and when prompted for a password, enter the word "null". Afterward, set up a new pattern.

Alternatively, The G2/Hero's 'Forgot Pattern?' screen asks you to enter the Gmail address you signed in with and its password.

Here is another trick rather hard to describe as I can't write it in this forum. You know the letter x. Try writing it 3 times before the @ sign in the following two items below.

If you enter @gmail.com and then the password, then it will say it's not right. You need to enter @googlemail.com and then it will accept it the password, purportedly.

If you have forgotten the screen unlock pattern, you have up to five attempts to try and unlock your phone. If this fails, you can unlock HTC Inspire 4G by entering your Google Account user name and password.

1. On the unlock screen, attempt to enter your unlock pattern five times.
2. When prompted to wait for 30 seconds, tap OK.
3. If the display goes off, press the POWER button to turn the display back on, and then press the bar on the lock screen and slide your finger down to unlock the screen.
4. Tap the Forgot Pattern button in the lower right corner when it appears.
5. Enter your Google Account name and password, and then tap Sign in.

You are then prompted to create a new screen unlock pattern. If you no longer want to use a screen unlock pattern to secure your phone, tap Cancel.
Follow that instruction step by step and if you success you get your HTC unlocked, remember read that instruction carefully, if you did wrong step you will not allowed to enter your google account.

It says Emergency Calls means it locked to Network Lock,You need to Unlock it from Network Lock,You can get the Unlock code at
http://www.mobileunlocksolutions.com/htc-touch-hd/rs1wp9/ and Unlock it,Then You can get the password code from service provider as free of cost,.

Exactly how are you locked out? If you're stuck on the lock-out screen with a lockout pattern that you've forgotten? If that's the case, the G1 manual indicates the following:
"When you fail to draw the correct unlock pattern on the screen after five attempts, you will be prompted to wait for 30 seconds before you can try again. If you forgot your screen unlock pattern, touch Forgot pattern. You will be prompted to sign in using your Google Account name and password, and create a new screen unlock pattern before the Home screen displays."