I have a wall socket in my kitchen but there isn't enough cable leaving the wall to attach a new RJ45 jack to (There's about an inch left to play with). There's no slack in the cable so I cannot pull more through. is there a way to extend the cable within the wall socket?
You should have enough room to wire a keystone style jack on the remaining cable. Once you have the jack on the end of the cable, you then snap it into the wall plate. It will be easier to do this than try and wire the remaining amount of cable to a RJ45 wall plate. Note, most home improvement stores will have the network parts you need.
If that will not work and you don't have the means to run a new wire you will need to use an extension. Note, this should be last resort. Attach a keystone jack to the end of the cable that will just float in the wall. Then make a short one foot cable, or cut a network cable you already have, with a RJ45 terminator on one end. Connect the short length to the jack that is floating in the wall and then wire your network plate to it. This method will introduce introduce interference on the line and if the run is already near its max then it might make the connection unstable/slow/unusable.
Correct solution - replace the wire with a long enough wire. This plays to "why network & telephone wires should always be run in conduit, always."
Kludge that will still be difficult with only an inch inside a box - put a plug on it and use a dual-jack extender.
Kludge that will work fine if you are OK with drywall and paint repairs - move the box 4" up the wall.
You really should not attempt this, but if else fails, you should try this:
Is there a way you can attach a new cable at the old one and pull a new cable through the pipes?
Some tools: Connector tool.
Sometimes if you unplug the other end of the cable, you can get enough slack to put a terminator or jack on the end of the cable. Then run a small bit of cable into the box.
Alternately, get an 8-way terminal block: http://www.newark.com/cinch/8-141/terminal-block-8way/dp/28F717 and use this to bridge the wire to another length of wire. Then screw the terminal block to the sheetrock or to a stud.
Finally, you could also get a piece of protoboard, solder all 8 wires into the protoboard, and solder 8 wires from another piece of ethernet cable to join to the first piece. Easy enough to do