base minimum tv's still have vga ports and maaaybe a 3.5mm audio plug or a stereo rca plug near the vga input for audio.
it's component level quality but largely good enough for most videos, and is the cheapest method aside from buying a new video card.
unless the intel video doesn't support video acceleration then you need something like an a low end amd/nvidia card with hdmi output.Sapphire hd5450 low profile gpu
for $24.99 with $10mir to come out to $14.99 with free shipping before tax.
probably the best new cheap card you can purchase on newegg, with audio output over hdmi.
the card is rated around 6w idle and 19w max power consumption wise according to wikipedia's amd gpu list.
probably drinking some tea.