Aleš
It must be stuck in the inbox database then.
There isn't anything else in the registry.
In Inbox ensure that in the Address tab in options none of the services are ticked.
If you have a backup created when it was working, I recommend restoring back to it.
What I think has happened is that you have a slightly corrupted Inbox and MSMail database on the device. The message parameters are displaying still so the Inbox app is attempting to read them.
You could try recreating the accounts bit perfect, resynching them with the mail server, clearing it out - including manually emptying the large attachments folder in \Program Files\Applications. Then deleting them again.
I had a rummage around my Inbox detabase and there are a number of corrupted email entries still sitting in there for quite some time back. They don't exist in Inbox itself.
The difficulty here is that deleting the data from the inbox database is not a good idea. You'll most likely break the index and force a hard reset.
Second option is to delete the inbox database completly. However I'm very sure that doing so will cause fire and brimstone to reign from the sky, as its a process called pagstart creates these databases - and that only runs at first boot. If CE refuses to recreate it afterwards, you'll have to hard reset anyway to get it back.
I also have found this utility that runs a repair operation on the ce3 inbox:
http://www.casio.com/downloads/consumer_devices/inboxrepair.zip
It isn't for hpc2000. It may work, it may not. It may make things worse. I don't know. Everything here is your call.