google will not ask for your phone number if you provide a secondary email when you register. I've done that a lot of times. With regards on your problem, you can try to use proxy and try if you can now register another account on gmail.
May be you are using a common ip. Try reconnecting your internet connection. Ask for a stand alone ip address from your ISP.
it was happening same with me also, few days ago, but now it works fine and i am able to create new gmail account, some days ago gmail was asking for phone varification, and when i put my phone number i never get code on my mobile.
Just make sure that you don't open more than one account per IP every 24 hours and you should be fine. If not, wait a couple of days, or get a new IP.
It happens many time when some one create many gmail accounts from one IP.. but it is temporary.. try aftr 10/15 days.. it will allow u..