Timer with monitor

For the "timer with monitor" (i.e. no control, I presume you have got that portion already sorted), if you can code (or are willing to learn) then this is possible using an Arduino board, and a display. The devil is in the detail though (for instance, you might wish it to continue operating during power outages etc). There are ready-made products, either known as timer/counters, or known as data loggers. You're looking at hundreds of $ upward though, for those products.

Or you could try to repurpose existing clocks or timer boards, as discussed in the blogs here:

 Process Duration Timer  Blog 1 (The Timer) 

 Building a Process Duration Timer into a upscale Case 

If it were me, I'd spend some time learning Arduino, because it is knowledge that you will then be able to re-apply to other problems in future too. There are plenty of Arduino learning sites and books, to help beginners.

Hi invitech - if I was doing this I would use discrete components, where the word 'discrete' includes relatively simple LSI and MSI digital integrated circuits. However you go about it you will need a clock signal. If the unit is mains-powered you could obtain 50Hz square waves using a small isolating transformer to drop the mains voltage down from 230v to 3v AC, and a simple comparator chip to turn the resultant sine waves into square waves of about 5v peak-to-peak. Ideally you need an oscilloscope to check the volage of the 5v p-p from the transformer before connecting it to the comparator. Watch out for those mains voltages, they can be lethal. The output of the clock circuit can be connected via an AND gate (see below) to the CLK input of a suitable programmable counter chip that will count up to the maximum value required. This will depend on the battery capacity and how much current you will be pushing through it on charge, or the amount you will be draining from it during discharge. The outputs from the counter chip will go to a chip that converts a digital value to the pattern required to drive a 7-segment multi-digit display. A 'Stop/Go' switch will be needed, when it is in the 'Stop' position the RST pin on the counter needs to be held in the RESET state. When you switch to 'Go' the RST pin will change state and allow counting to start from zero.

Waiting in the wings will be another comparator. One input will be monitoring the battery voltage, the other will be monitoring the voltage from a suitable 28 VDC reference supply. This will need scaling down to suit the max input to the comparator. The design of the reference supply depends on how accurate you want it to be. I found that band-gap references did the job. You will need to scale down the 28VDC from the battery to match.

One input of the AND gate (see above) will be connected to the scaled-down 28VDC from the battery, the other input to this gate will come from the clock circuit. By this means the clock will stop when the battery voltage reaches 28V DC.

Measuring discharge time follows much the same system. You'll need a 16VDC reference, and an inverter on the battery-voltage signal to the second comparator so that counting starts at anything higher than 18V and stops when it gets down to 16V DC.

Sorry the above is a bit sketchy in places, it's been a long day... 

You’ve not mentioned what level of accuracy you are after because solutions could range from simple to complex based on this alone.  I would have thought nearest second would be good enough which almost certainly means you could get a simple solution accurate to sub-second.  If you’re after millisecond accuracy then that’s likely more difficult.  Also, is this just a home project or product development?