What is that gmail account you need to access? Yours? someone else's.
If it is your account, you have full access. Your say you can sign in to it. If it is not your account and you NEED to access it because of your job (police for example) ask a judge to sign an authorization.
Make sure that the connector fits both Male/Female ports on the monitor and computer match. Then make sure that the software is installed properly. If the cords don't match, go to your local best buy or tech store and purchase an adapter.
As an alternative, you can try making a new Time Machine backup from the files of the old HDD. Install Mavericks from scratch on the SSD and then transfer the documents needed back from the Time Machine.
I would recommend installing fresh OS X when upgrading from HDD to SSD anyway.
Here is how to make a bootable USB stick for installing Mavericks:
http://www.youtube.com/watch?v=2or1Wthkl1w
Do you need any additional assistance?
In other words it's not turning on with the battery? In other words the battery is dead? If it works plugged in, it's either a problem with the battery, (by far the most likely,) or the connector. (In rare cases it can be a small card inside;)
ifixit.com is the best place to go to troubleshoot; we need more information to help you...
GET THIS FIRST http://www.malwarebytes.org/ CLEAN IT I T S SAFE THE DEFRAG THE PC FOUND THE DEFRAGMENTACION IN ALL PROGRAM SISTEM TOOLS DEFRAG C AND D SEE WHAT HAPPEN
The screen, the cable that connects to the screen or something internal has taken a hit. You'll need to get it serviced to find out which. Sorry, but there's not much diagnosis we can do from a distance.
With the limited information you have provided, the best thing I can recommend is going to Mail preferences (click 'Mail' on the menu bar, right next to the apple icon at the top left corner, and then select 'Preferences...'). Then go to the 'Accounts' tab, select the problematic account on the left and then click the '-' button at the bottom of the screen. This will remove the account and any settings you have saved for it. After you've removed it, click in the '+' button and fill in the information in order to add your account again. Your messages will be downloaded (you won't lose any of them in the process) and if the problem was caused by a setting, it should be fixed now.
Check to make certain you entered your username and password correctly. Then, delete all your unimportant email from your "inbox" and your "sent items" folder, then empty your "Trash" folder.
Try launching it from the application in the apps folder. If that works, get rid of the icon in the dock and add a new one from the working application.
Depending on the version of OSX you are running, iCloud may not be available. Click the Apple icon and Software Update. Hopefully you have an update waiting for you, good luck. :)