Unable to set up Google Apps email account in Mac Mail

I have an email address for my domain that runs through Google Apps. I was using it without any problems through Thunderbird on my Mac until it stopped sending email last week. I could retrieve emails, but I could not send anything. I would get an "SMTP connection timed out" error message. There was no problem (still is no problem) sending or receiving email if I login to my account on my web browser. After pursuing several fruitless "fixes" for Thunderbird, I tried the last option, which was to delete the account, then reinstall it. Well, that's when the real trouble began. After deleting, Thunderbird would not allow me to add the account back in, saying my password was incorrect for the account. The password is totally correct. It works in my browser! I followed a bunch of different threads on Google, including ones that say to double- and triple-check the SMTP settings and make sure the full username is included. I've done all that. No success. I'm also NOT using 2-step authentication, so that's not the issue here.

As a last resort, I decided to set up this account on Mac's Mail program, hoping I'd have better results. Nope. I cannot add this account to Mac Mail, either. I am entering all the settings correctly (it prompts me to enter them manually after it tried to do it automatically). It basically says it cannot get into the server with my credentials, even though my username and password are correct.

I am at my wit's end. I really do not want to have to use my browser every time to access this email account, particularly as Thunderbird has a bunch of offline folders that are used for organizing my incoming mail.

Can anyone assist? I can already tell you that I've tried the fixes at Google Groups and none of them work.

Thanks,

Jennie