With the current infrastructure available to SETI, how distant would it be feasible to pick up routine radio communications and noise from a planet emitting radio with identical power and signal characteristics to that of present-day Earth?
Using current technology (and by that I mean experiments and telescopes that are available now) we would probably be unable to detect life on Earth even if observed from a distance of a few light years.
A "blind" search could look for radio signatures and of course this is what SETI has been doing. If we are talking about detecting "Earth-like" signals, then we must assume that we are not talking about deliberate beamed attempts at communication, and so must rely on detecting random radio "chatter" and accidental signals generated by our civilisation.
The SETI Phoenix project was the most advanced search for radio signals from other intelligent life. Quoting from Cullers et al. (2000): "Typical signals, as opposed to our strongest signals fall below the detection threshold of most surveys, even if the signal were to originate from the nearest star". Quoting from Tarter (2001): "At current levels of sensitivity, targeted microwave searches could detect the equivalent power of strong TV transmitters at a distance of 1 light year (within which there are no other stars)...". The equivocation in these statements is due to the fact that we do emit stronger beamed signals in certain well-defined directions, for example to conduct metrology in the solar system using radar. Such signals have been calculated to be observable over a thousand light years or more. But these signals are brief, beamed into an extremely narrow angle and unlikely to be repeated. You would have to be very lucky to be observing in the right direction at the right time if you were performing targeted searches.
It has been suggested that new radio telescope projects and technology like the Square Kilometre Array may be capable of serendipitously detecting radio "chatter" out to distances of 50 pc ($\sim 150$ light years) - see Loeb & Zaldarriaga (2007). This array, due to begin full operation some time after 2025 could also monitor a multitude of directions at once for beamed signals. A good overview of what might be possible in the near future is given by Tarter et al. (2009).
A brief search led me to the conference proceedings for the "Life in the Universe" conference held at Ames Research Centre in 1979 (yes, this is old, but serves as a good baseline from which to begin). The paper "Eavesdropping Mode and Radio Leakage from Earth" notes that early warning systems for ballistic missiles beam intense radio signals that could be detected up to 15 light years away. It is also mentioned that the proposed radio array for Project Cyclops would have been detectable up to 250 light years away.
Of course this does not answer your question regarding "present day Earth". This 2012 article from The Straight Dope is certainly rather opinionated but the author throws out an estimate of 30-50 light years. They also mention that radio astronomy signals being used to survey the sky might be detectable up to 1000 light years away (citing Seth Shostak of SETI).