In the absence of more precise information, here are a few thoughts. I think there may be some confusion here regarding the difference between Minimum CPC and Maximum CPC. There may also be some confusion regarding the difference between Maximum CPC and daily budget.
* First, it sounds as if both the daily budget and the Maximum CPC may have been set to $35.00. Possible? (As an aside, it is a good practice to never set one's Maximum CPC to an amount higher than you one would actually wish to pay for a click.)
* Maximum CPC is set at the Ad Group level, and controls the most one may spend for a click.
* Daily budget is set at the campaign level and controls the maximum amount of clicks that all Ad Groups within that campaign may accrue in a 24 day.
* Minimum CPC and Maximum CPC are not the same thing:
* Maximum CPC is set by the advertiser, and defines a cap beyond which the cost per click may not go.
* Minimum CPC is defined by the AdWords system, per keyword, and is not a fixed amount. It varies according to the Quality Score of that keyword as used in that particular account. Depending on Quality Score, Minimum CPC can go either up or down over time.
* When Minimum CPC is adjusted by the system on the basis of Quality Score, it uses as its upper limit the Maximum CPC that was set by the advertiser. If the Minimum CPC goes higher than the Maximum CPC set by the advertiser, then the keyword will become 'Inactive for search' (as implied by poster_boy earlier).
* In the particular case being discussed here, if the Maximum CPC had been set to $35.00, then the Minimum CPC could go as high as that - but not beyond.
Hope that helps to bring some clarity. More than likely, it'll take a look at the account to get to the bottom of this - and I hope you get a response shortly, crak_bot.