The symptoms sound like sticky shed but according to the info I have, Scotch 102 isn't included in the tape formulas that commonly have this problem. In fact, 102 is a very old formulation (introduced in 1953) on Polyester backing. Is it possible that 102 is just what the reel says and that some other tape (maybe not even 3M) is on the reels you're trying to play? From the description you gave, 102 would indeed be brown on both sides.
The tapes may respond to baking and if so, they are by definition, afflicted by sticky shed syndrome. There is a more general classification, Soft Binder Syndrome and tapes that exhibit the same symptoms but
do not respond to baking are classified this way. The causes of this problem are many but the results are, squealing, and the deposit of sticky residue on all fixed elements of the tape path.
Possible ways to get a decent play of these tapes include, wet playing and cold playing. Needless to say, these techniques require dedicated playback systems for just this use and about the only folks who might have access to these systems are professional restoration studios.
The bottom line here is that with a reasonable outlay of cash, you can buy a food dehydrator and you may and get a week or so of playback of these tapes before they turn sticky again.
If the tapes important, it would probably be better to enlist the aid of a professional.
There is some info regarding tape problems in the "Beginners Guide" located in a sticky above the General forum.
If you'd like to try baking, here's a link (which is also located in the ",..Guide").
http://www.tangible-technology.com/