This was a blunder on your part and if there are no editing facilities in the site then it becomes a problem as how to enter the site for applying or convince the authorities that it was done inadvertently. The only thing one can try is to send a personal application to the coordinator of the exam at the address provided in the site or send an email explaining the problem and asking to make change in the system by the system administrator so that you can apply as a fresh candidate. You say that they are not responding to your email so in that case send them a reminder and send a physical application also to their address. Keep a copy of the all of the correspondences with you so that if they ask you then you can produce it to show that you were active just after knowing your mistake.
If you were trying to apply in Himachal Pradesh public services then their contact information is -
Himachal Pradesh Public Service Commission, Nigam Vihar, Shimla, H.P. - 171002
Enquiry ph. - 0177 - 2624313
Toll Free No. - 1800-180-8004
(Any working day between 10.00 AM to 05.00 PM)
If that does not help you can interact and communicate with some high officials there who are sometimes very helpful to the candidates and you must try this channel. Some of the officials and their contact numbers as given in the site are -
1. Shri Ajay Kumar, IFS (Retd.), Chairman, Ph: 2623793
2. Dr. Rachna Gupta (Former Editor, National Daily), Member, Ph: 2623796
3. Shri Ashutosh Garg, IAS, Secretary, Ph: 2623786
4. Ms. Ekta Kapta, HAS, Joint.Secretary, Ph: 2623857
5. Shri Rakesh Verma, Dy.Secretary, Ph: 2622015
6. Shri Yog Raj Sharma, Under Secretary, Ph: 2622015
Knowledge is power.