Is it possible for one to connect a telephone cable to light up a light-bulb?
It is possible to connect a telephone cable to light up a light-bulb (assuming that you mean the cable from a "Central Office" telephone exchange or a PBX system) BUT
Central Office telephone systems use 50 volt supplies. Anything below about 100,000 ohms may cause problems and even that is marginal.
Available current at 100k would be 50/100k = 0.5 mA.
At 0.5 mA the available energy is V x I = 50 x 0.5 mA = 25 mW.
If you are prepared to draw as much power from a line as possible it will depend on how far you are away - but you may get tens of mA. Central Office systems are typically 50V. PBX may be 25V and possibly other voltages.
I forget typical feed resistances by a figure of 600 ohms comes to mind. You get maximum load power when you load to half voltage (maximum power transfer theorum) so at say 600 ohm load, 25V Power = V^2/R = 625/600 or about 1 Watt.
Not so good for a bulb - good for many things with an LED.
BUT telephone circuits may shut the line circuit down if it sees this sort of loading.
There was a convention, used by certain Princess Phones, that provided power on the non-tip-and-ring pair. This was not central office power, but provided by a local transformer, that provided DC power for a light. Your phone has to be specifically wired this way to expect 12V power on the black and yellow wires, leaving red/green for tip and ring.
In the modern era, this is difficult, because of two-line phones being more common, as they use the black/yellow wires for a second phone line.
http://www.oldphones.com/servlet/Detail?no=48 shows an example of this kind of power arrangement.
Entirely different story when you refer to a VOIP environment with Power over Ethernet, which can deliver roughly some 35 - 60VDC at several hunderds of mA.