The PassatWorld forum link above is a life-saver for the owners of older Passats (I have a 2004 and have saved thousands of $ already from it) and you could learn a lot there.
The funny lighting pattern from your shifter is telling you the transmission is in “limp” mode, meaning the electronics that regulate some of its functions think something may be wrong and are trying to protect it from damage.
It could involve a transmission fluid problem, as suggested by db4690. If that is the case, you might best be served by finding an independent mechanic who specializes in VW’s. This transmission is very solid, but very finicky about the fluid it uses: unfortunately, the expensive VW fluid or one made by Pentosin (same stuff, notably cheaper with that label) are the only ones most knowledgeable owners pretty much insist on. And the filling procedure involves something like a Celtic ritual (car perfectly level, fluid at exactly the right temperature and fill until it’s just overflowing. Really!) Over or underfill - you’re guaranteed further issues. Expect a several hundred dollar bill just to change it.
A second, insidious possibility involves water leaks and is another reason you need a guy who knows these cars in particular. The electronics that regulate the transmission (“transmission control module” or TCM) are, conveniently enough, under the carpet on the floor beneath the passenger seat. Right where water from leaking pollen filters, clogged sunroof drains, or seals on the inside of the doors tends to pool. I’m not saying this is happening to you, but a drowning TCM is another possibility that needs to be at least considered. If that’s the case, you need to fix the underlying water problem, too.