Comment on Duplicate Content Penalty SEO by SEO Dave.
I see, sounds like you are sorting out a mess, loosing control of your old domain and fixing the issue by creating a new domain. Valuable lesson, NEVER allow others to own your domain, always register the domain yourself and have access to the domain registration account.
If the old domain remains deleted Google will probably index the new domain after you add some backlinks to it (I assume you haven’t built new backlinks yet?), but you won’t gain your old rankings automatically without the 301 redirects.
With the 301 redirects Google will treat the new domain as deserving whatever rankings the old domain had minus a small downgrade for the redirects.
Without the 301 redirects it’s like me making a copy of your website and placing it on a new domain and hoping I can beat your website rankings just by copying your website. The only plus you have is the old domain is delete (so only one copy online), BUT this only helps if your SERPs are SUPER easy.
If you consider a good SERP “Alfain Advertising & Publishing” you’ll probably regain it easy, but if you had even semi-competitive SERPs like “Advertising Agencies in Dubai” and “Advertising Agencies in Sharjah” (I’m guessing you didn’t have those SERPs with the old site, your SEO is really bad) you will be competing with competition who have been online longer than your new domain and have backlinks.
Basically you just shot yourself in the face deleting your old domain without adding 301 redirects. Saying that I’d be surprised if the old domain generated 50 visitors a month from organic search, so not lost a lot (unless you can make a living from so little traffic).
The fix is gain control over the old domain and pay for another year domain registration and 301 redirect (or use the old domain even better fix). If you have lost control of the old domain it’s a case of fingers crossed and rebuild like you would with a new website.
Your current SEO is rubbish and doesn’t look like you have a backlink profile (backlinks are important), so if this was easy SERPs you had (company name type SERPs like “Alfain Advertising & Publishing”) with a better SEO design and working on backlinks you should easily regain the SERPs.
Search Google for Alfain Advertising & Publishing and you are at number 1 today. You should signup for Google Webmaster Tools and check the index status there, will be 100% accurate what is and isn’t indexed and if Google does hit the site with a penalty you sometimes get a warning via Webmaster Tools.