I have a standard monitor port on the pc and av in on the lcd can i directly connect them?
Also how can i power the pc?
As you have described them you cannot directly connect the PC to the LCD.
The standard PC output port is VGA, a 3 row D type connector. If the LCD does not have a VGA input, then you cannot use this connection.
If the LCD does not have a VGA connector, it will probably have a composite video input, normally a phono connection. If your PC does not have this output, you cannot connect via this either.
You could get a video card for the PC with both VGA and composite out. Easy. However, as said by E_T_V the picture quality on composite is pretty rubbish when compared to VGA.
I would recommend looking for a small LCD with VGA input. Difficult.
You can power the PC two ways.
Throw away the PC internal power supply and shop around for a special one that works off 12 volts. Difficult.
Buy a 12 volt - 240 volt inverter. These are available from Maplin. As long as you specify one with adequate power, this will power the PC. Easy.