Hi Tim!
Yes, you can remove and reinstall MSDTC 'underneath' SQL.
However, the health of this cluster sounds pretty suspect!
I would caution you to BACK EVERYTHING UP before you do anything to this
cluster.
:-)
All system db's...everything.
If it's not moving, back it up!

Ok, with that said, you can follow this KB article on moving and rebuilding
the MSDTC resource:
294209 How to rebuild or move MSDTC used with a SQL failover cluster
There is also this article:
Microsoft Distributed Transaction Coordinator (MSDTC) Recovery Techniques
in Windows 2000 Cluster Server (243204)
Which is not really SQL specific.

As for the FTSearch issue...that is a little more complicated.
Generally there are two reasons FTS doesn't work in a cluster.
1. Search setup was not successful
2. You have missing registry keys.

For number 1, you will need to do some detective work.
First collect the most recent sqlstp#.log from both nodes.
Look for the searchsetup.exe section.
Any errors? If there is an error number, go to a cmd prompt, type net
helpmsg <errornumber>
What's the error? This will be important. At that point you should engage
PSS to rebuild FTS, as it's tricky at best.

For number 2, follow this article to confirm you have the correct registry
entries for FTS:
http://support.microsoft.com/default...B;EN-US;810056
INF: You Must Use Resource-Specific Registry Keys for SQL Server Cluster
Resources (810056)

If missing, put them in there. If that doesn't fix it, again, call PSS,
you probably have more at play than just missing registry keys.

Hope your sickly cluster recovers!
Thanks!
Donna Lambert
SQL Server Product Support