How frustrating. Discs written with packet writing software such as InCD and Direct CD can be rather vulnerable to problems, not least as one problem during a packet writing session can leave the entire disc unreadable.
Unless you absolutely need 'drive letter' access - that is treating your CD or DVD writer like a large floppy - you get a more robust result using mastering software (like the main Nero program), as you don't need special software to read the results. Discs written using the main Nero program and similar should work on any drive that can read the media type you've used without any special software installed. This is true even when using rewritable media - you can always erase the rewritable disc to use it again, though the only thing you can do is to erase and reuse the disc - you can't erase files selectively unless you're using multisession (which can bring its own problems).
Anyway, that's advice for the future - for now, you want to try to get at your files on your existing discs if you can.
Are you using the same drive as you used to write the discs to try to read from them? Did you ever read back data from your InCD discs before the reformat successfully? Is it just one disc, or several discs? If you've reinstalled InCD, can you format a new disc, write some files to it, remove it, reinsert it, and read back the files? Have you got a separate reader on your computer - and if so, do the discs work in that rather than your writer?
What happens if you uninstall the reader program and install the version of InCD you were using (having both InCD and the reader installed simultaneously is almost certainly unwise)? I can only find InCD 220.127.116.11 for download now; I don't know whether or not that needs a Nero 6 serial number to work.
If you can't persuade InCD to work, there's two versions of the reader to download at ftp://ftp6.nero.com/ - I suspect EasyWriteReader.exe is for InCD 3 and EasyWriteReader4.exe is for InCD 4. I'd try them in that order - the one without the 4 in the file name first (uninstall InCD and any other versions of the reader program before trying another).
This is just what occurs to me - maybe someone with some actual experience of your situation will be able to help, especially if you provide more details of your setup (especially what version of Windows you've installed, also the make, model and firmware version of the writer).
For the future, I suggest you write all important data to CD in ISO format using Nero. If you have a DVD writer, choose whichever DVD format works for you (I tend to use UDF for all my data DVDs - I only need read compatibility with Windows 2000 and Windows XP, and UDF frees me from the 2GB limit per file, so I tend to write all my DVDs as UDF rather than ISO or UDF/ISO bridge).
Consider using the arguably more robust write once media for files you don't want to lose, ideally checking the discs in a separate reader, and, if the data is important, making at least two copies. You can always archive the discs - even decent branded CD-R media is pretty cheap these days, whereas lost data is often irreplaceable.