Hi,
it is the time to go with Murphy: 

"if all attempts (to repair something) failed,
it is time to read the documentation".



There are recovery procedures described in admin guide
even for scenario like yours.

Basically you will have to configure your server so as it previously
was,
define drives and libraries, 
define and format DB and LOG files (their volumes can have different
names and
paths then before crash, they only have to be large enough),
and then perform DB restore.

It is possible to find out what kind of database backup 
(full, incremental, which version of incremental) 
is on which tape by letting the stand-alone "dsmserv" command
have a look at each tape concerned.
I have forgotten the proper syntax, but is simple and
documented either in Administrators Reference
or in Administrators Guide.

If you used full/incremental approach for DB Backup, you will have to
restore
last full backup first, after that all incremental ones and do not
forget 
to tell commit=yes along with last tape.

All file backups performed after last DB Backup are lost,
since your TSM Logfile is lost.

After the restore you will have to perform Audit volume for all volumes
changed
since last DB Backup. Well, since you have not saved your Volhist,
you only can guess which volumes changed. 
So audit all volumes, if you can afford the time.


Purchase much coffee and a couple of pizza´s,
give few important documentation chapters a chance to be read by you,
set your valuable tapes to read-only
and go on!

Good luck!
Juraj