how do i check if i have an integrated modem?
The notebook does not support internal modem.
It support Bluetooth and WLan
If the notebook would support modem then you should find a modem port (RJ-11) at the notebook’s side.
as for the hdmi, the end of the cable that connects to the tv needs to b hdmi but on my notebook the socket i have is a mini port, so what do u call the cable that has miniport on one end and hdmi on the other?
The notebook support VGA (RGB port) . This port can be used in order to connect an external monitor.
There is No DVI but you could use an Dockingstation which support an DVI port. This would allows you to connect to the HDMI port of HD TV. In such case you could use an DVI to HDMI cable.
But note; DVI transmits just video signal. if you want to have audio/sound via TV speakers then you would need additional audio cable to connect the notebook’s headphone jack to TV.