Is there a problem if there are zeroes in a time series?

Prior to developing a model, my series has zeroes at the start (2 values) and interspersed throughout. The series also expresses seasonality with period 52 weeks. Someone told me to fill in the first two values with the values from the same period in the following year. Not sure if that's valid. I'm unsure about how to proceed here.

Is there a limit to how many zeroes a series may have before it becomes "unmodelable"?

Thanks all.

What system are you working with? Biometric, military etc.

It's financial ... a time series of expenditures. As an example ...
0,0,0,55,4545,1233,634,0,36,0,1234,8636,...etc.

Seven years of data with a period of 52 weeks. I was told, for the first three zero values, to replace them with next year's values in the same period. Is that correct? What about autocorrelation issues if there are a number of zero values interspersed throughout the series. How do I build the model is really my question?