You would certainly need an RCA Analog to Optical digital converter just to get 'stereo' TV audio out to the Beam. If it were me I would not bother, as you perhaps could get reasonable sound with a cheaper PCM stereo soundbar instead. The TV is rather old (14 years +), so I would maybe look to upgrade the TV first.
Perhaps now is the time whilst the current Black Friday sales are still on.
Another option - if the PC has an optical audio port, then you could use that with the optical adapter, Not sure if you’d get lip sync issues or not.
I would go with an HDMI switch with an optical output port, and insert it between your sources and TV. There are many threads about these in the Home Theater section of the forum.