I can relate to the sentimental value. I bought my '89 on Feb 29, 1996. It was a low-mileage NA, in beautiful shape.
Now, almost 18 years later, it's got a 7M-GTE, R154, 3.909:1 differential, and until it developed rod knock last year, had loads of power, but the half million kilometers have taken a toll on the body.
As far as sentimental value... I'm going to fix it up. It's going to be WAY too much work, about a minus 5 on the 1 to 10 practicality scale. This is fueled by 2 things. One is that I want to learn how to do some of the stuff that I'll need to do to fix it and the other is my daughter, and some history. My daughter has always known this car. It's been around her whole life, and she loves it. The history is that I remember my father's 1969 Buick Riviera, and although I didn't know that car my whole life (He bought it used when I was 8) I certainly loved it. I have never really forgiven him for selling it when I was 17.
So, the '89 stays as a project car. My daughter is going to learn a lot about fixing and working on cars helping me restore it (That is... If she ever wants to drive it she will.)
I didn't really think that Supra could be replaced... But I'm slipping into my 1990 Targa pretty comfortably. I certainly missed some of the things that I'd done to my '89 to make it suit me better, but I'm slowly yet surely bringing it into line. Little things, like the TRD shift knob, climate control LEDs. Bigger things like the huge turbo, boost control and the like are a bit longer in getting ready, but they're coming. The newer Supra feels (not surprisingly) just like the old one, very familiar, and very comfortable. (Though I still haven't gotten used to the whole targa shake thing. That kinda weirds me out. A Supra shouldn't DO that.) It probably helps that they're both medium grey on 3E5 red, but I'm sure that I'd get used to a different colour scheme fast enough.)
So... If you can't/won't fix it, by all means sell it. Even with high sentimental value, it's still replaceable. I believe that you'll find that what you're really attached to is a Mk3 Supra, not necessarily the one with that VIN.