Hi Praveena
I suppose there shouldn't be any issue if you are using the Ad unit id from the Old AdMob UI. This needs some explanation. In the old UI, each app had its own publisher ID ( which is the Ad Unit ID now). But in the New UI, there is a single publisher ID for whole of your account.
I have integrated Google Play services based AdMob SDK into my app with the old per app publisher ID and it shows Ads.
So I would suggest you see in your logcat, what specific error is causing the non-display of Ads. Please post it here.
Best,
Kunal