Yeah... It did boot up a couple of years ago when I last plugged it in, though, so there's still hope! :)
Could just recap it. I did an Apple a while back. Was not hard.
The RIFA X2 capacitors in the PSU tend to explode. I opened mine up and was lucky to find that my BBC is one of the few later revisions that don't use these. Well worth checking though.
The failing electrolytic capacitor syndrome is interesting to me because I worked as a hardware designer in that period and I don't remember it being common knowledge that those components had a limited life. I do recall that we mostly used solid Tantalum capacitors with the transition to surface mount technology but I believe that was more to do with survival in the production process than long field life time.
It is really easy to connect a Beeb to SCART.
Be careful with the TTL RGB levels, though. You should add some resistors.