How can I sign up my client for their own Soundcloud account

https://kyurious.me/

Are you trying to view it both on browser or on an email client. if it is in browser then click on the thumbnail on right corner which displays your profile pic and there is an option of add account and then you can sign in with another gmail account

Refer to the Youtube Video

Point your web browser at http://www.gmail.com

If another account comes up, sign out of it by clicking the avatar in the upper-right then clicking "Sign out."

If you then still can't sign in to your account, click the "Can't access your account?" link on the sign-in page.

it sounds like you are BT customer. if you want to use their email (don't, instead, open up a Gmail account and route your things there but:) then BT can help you with the email client settings. if you can log on here https://signin1.bt.com/login/emailloginform then your account is okay. the Mac Mail is an email client, it needs to be set to log onto BT Mail. For that BT has to authorize the access, so they have the instructions how to set up mail. Likely, that you need to create an Account, similar to Yahoo that has a port number and secure logon setting. Likely, they send this page to you: http://bt.custhelp.com/app/answers/detail/a_id/9962
Anyway, not a Mac problem...

You can still go to the web browser (Safari) and go to the web version of your mail client.
If you insist on having it set up as a desktop client, you'll use the mail program. When you open it for the first time, it will ask for all the info to set it up from your pre-existing email account.

On the SoundCloud sign in page, click on the "Forgot your password?" link.

I'm assuming you're trying to sign up for a new Twitter account with a new email address? Unfortunately Twitter won't allow you to sign up for a new account with the same email address as the old account.
If you're trying with a new email address, it sounds like you have a cookie from Twitter that is "remembering" your old account. Try this: After deactivating your account again, go into your browser settings and delete your cookies. The instructions will vary based on the browser you're using, but below are the instructions for Internet Explorer.

• Go to Tools - Internet Options. If you don't see Tools, look for a gear icon in the upper-right of your browser window.
• On the General tab, click Delete.
• In the window that pops-up, make sure Cookies is checkmarked and click Delete.

I'm not sure if Yahoo messenger has the specific ability to log in to two accounts simultaniously. If you don't mind using another client to log into your Yahoo account, there are a lot of third party messaging clients (Trillian, Pidgin, Spark, Meebo, etc) that will let you log into multiple accounts at once. These will also let you sign into other protocols such as AOL IM, MSN messenger, ICQ, IRC, Yahoo IM, and several others.
If you're open to trying a new client, I'd recommend trying Pidgin: http://www.pidgin.im/download/
Its probably one of the easier clients to learn to use.
If installing new software is an issue, use one instance of Yahoo Messenger and a web client like https://imo.im/
Please leave feedback if this was helpful. Thanks.