Neville has an excellent response. We assume that you are talking about a battery electric vehicle (BEV) as there are several other possibilities for an EV. The cost to charge an electric vehicle is going to depend upon how much charge you need to put into the batteries, how large a capacity the batteries have, and the cost for the electricity. All these things can vary from location to location and vehicle to vehicle. For this reason we sometimes rely on a cost per distance traveled or over time.
Sometimes we need a cost per mile as Neville has suggested. Sometimes we are trying to determine a total cost per year or over the life cycle of the vehicle.1 What makes comparisons to petrol vehicles so difficult is that their major costs are in different areas. The operating cost for an electric vehicle is cheaper.
A petrol to electricity energy equivalency is one gallon of petrol equals approximately 33.4 KWh of electricity. In my area and many others electricity will cost slightly more for the same energy. But according to this analysis, (2) and others, the EV is more than 6 times more efficient than the ICE vehicle. Maintenance is also far less with electric drive than with an ICE drive train. As a result of the inherent nature of the EV drive and its efficiency, maintenance, fuel, energy and pollution will all be less than an ICE drive train.
The "dead battery" question is again only relevant to a BEV. A solar vehicle may only have to receive sunlight (3) and an online electric vehicle has its power transmitted to it.4 This is also a difficult question because it is very dependent upon rate of charge. A 70 amp 440 volt charge is going to be quicker than a 15 amp 115 volt charge (or less.) It will also depend upon the nature of the electrical storage. There are now buses that will complete a charge in under 5 minutes using ultra capacitors (5) or special batteries (6)
In general, you may hear a lot of misinformation and rumors regarding EV, but when presented with a specific issue there are existing specific solutions. It is difficult to respond to a rumor that "EV take as much fuel as an ICE" without a specific reference. It may be possible under some intrepretation of an isolated case but with electric vehicles 6 times more efficient than an ICE drivetrain it is rather unlikely.
There are many good sites and accurate reports among the rumors and false claims. Feel free to clarify your specific research requirements so that it will be possible to suggest additional sources.
"The [Tesla] Roadster's motor efficiency, battery-to-wheel, is 92% on average... For comparison, internal combustion engines have a tank-to-wheel efficiency of about 15%." http://www.absoluteastronomy.com/topics/...
See also mine at: http://answers.yahoo.com/question/index;_ylt=ArWR9oxF0Oia5_KBRIvMFgTsy6IX;_ylv=3?qid=20100209115723AAbYEhA