First you must decide which unit -- the TV or the Bose -- will be used to switch among your inputs. The Bose is clearly inadequate to the task; it doesn't do video switching at all, and it only has one digital audio input, a coaxial one. So immediately you're confronted with the necessity of connecting all your video sources to the TV, connecting one of your digital sources (the DVD or digital cable) into the Bose, and foregoing 5.0 sound from the other source, unless you buy some sort of external switcher.
(I say "5.0" because the Bose lacks a .1 channel; its "subwoofer" is no such thing, but rather simply a detached woofer that plays the bass from all channels simultaneously.)
Your other problem is that the Bose uses an RF remote. While that's superduper if you want to use it without line-of-sight, it complicates things when most other remotes on the planet use IR. There's probably a way to translate the IR codes from the Panasonic's or a third-party universal remote to the RF signals the Bose understands, but I don't know what it is.
Your problem here is that the Bose system is antiquated (it doesn't even do DTS) and inadequate to the task of integrating a home theater system with more than one source. If you can find somebody to give you $400 for it you could buy an Onkyo HT-S770 which, while no audiophile icon, still sounds better than the Bose and does everything a basic HT system should do, including switching all varieties of analog video, processing true 6.1 sound, and having enough inputs to handle all of your equipment and more.
And before you ask, no, you can't use the Bose speakers with a different receiver.
RichC