Some

[jack]

Are these correct?
1. I have problem with this computer. (What does this mean?)
2. I have some problem with this computer.
3. I have a problem with this computer.

What do these mean?
4. I have some problem with this computer. (What does this mean?)
5. I have some problems with this computer. (What does this mean?)

[Casiopea]

1. I have problem with this computer. :( Needs "a" or "-s")
2. I have some problem with this computer. :( Needs "-s")
3. I have a problem with this computer. :D (singular, one problem)
4. I have some problem with this computer. :( (Needs "-s")
5. I have some problems with this computer. :D (plural, a few problems)

Note that, 'problem' is a count noun, so either use "a" or add "-s". Also note, 'some' is plural, so the noun it modifies must be plural also, e.g., Count noun: some books; Non-count noun: some milk.

All the best, :D