Two forms on the same website, do not, in and of themselves, cause the problem you are experiencing. Of the top of my head, I would suggest two options to you.
One, check and see if you have fields in both your forms with the exact same name. If you do, that could be causing your problem. If there is no problem there, on to the next option.
Two, create a test page with only one form and create one field. Submit that form and the success or failure of that will tell very quickly if there is an issue other than the form. If the form submits, add in your fields and submit and check the results. There might one field causing the problem and this will identify the culprit.
Hope this works for you.