Does any player see the correct track durations? Have you tried a traditional hardware player (a stand-alone CD player, a car player, a CD boombox, etc)? What album is it and what is the record company? (I find this interesting because I am from Finland too.) If it is a relatively new release you should be able to get a replacement disc in case the problem is caused by a manufacturing error.
A cue sheet with tweaked INDEX 01 values should work, but you may need to import the album as a new library entry to get the correct durations imported.
If you really need to resort to "single file + cue" ripping and using an edited cue sheet and you want to create standard MP3 track files, don't initially use a lossy format like MP3. In MC you would need to re-encode the already lossy audio data and thus cause additional quality loss which may produce audible artifacts.
Preserve your edited cue sheet and re-rip the disc in e.g. the WAV format. Fix the filename in the cue sheet and import the cue album from a new folder. You can just drag and drop the cue file to MC's Playing Now list after you have moved the files to some other folder. In Playing Now you can select the cue tracks and convert them to MP3 track files.
EDIT
If you need help in editing the cue file, post it here and I can take a look. Keep in mind that the INDEX 01 values show minutes, seconds and CD sectors, not milliseconds. One second of CD audio occupies 75 sectors and the largest possible sector value is 74. For example, 14:21:65 means 14 minutes, 21 seconds, and 65 sectors (65/75 = about 867 milliseconds).
Alternatively, you can use an external audio editor for splitting the tacks. MC has its own Media Editor, but it is a bit limited. I can recommend the free
Wavosaur program. It is very powerful, yet small and quite easy to use. Also in this case you should start with a lossless source file. The best format for Wavosaur is WAV. Open the big WAV file and save the cutted tracks to separate WAV files. Tag and convert the resulting track files in MC.
