Hi Dennis,
If you are concerned with getting your data off the hard disk here is the method I use on clients systems.
You need a USB to hard disk adapter - I use the Ultra ULT40112 usb to ide/sata adapter, but a usb external disk unit will do the same provided you can connect your hard disk to it.
Remove your hard disk from your laptop and fit it to the adapter then plug it into a working OS/2 system - I'm assuming your partitions are all HPFS or JFS. This should allow them to be seen but not necessarily used. You should be able to run CHKDSK against each partition and then, hopefully, copy your data to a safe place.
I have used this method many times to recover data for clients - usually windows based. The one time I had to use it on an OS/2 system disk was a case very similar to yours, the the system partition would not boot and the unbacked up data was on the other partitions. It transpired that the disk was on its last legs with many bad sectors - I managed to move nearly everything from it over to a new disk.
To answer your last question. If you are certain that it is only system partition that is screwed then you might be able to just reinstall over it but be aware that that might not work which leaves you in the same state as now. If you have eCS or MCP DO NOT use fdisk unless you want to loose everything.
If you have the facilities for creating an OS/2 bootable CD with DFSee on it you should be able to check the file systems from the 'actions' menu, but as Raiko says - be careful.