When starting self-employed work, there are a number of consequences.
If the activity is gewerblich but not freiberuflich, it is necessary to register with the Gewerbeamt (~ trade office). This obligation is specificed in §14 GewO. Per §146 GewO, failure to perform a registration is a misdemeanour that can be fined with up to €1000. This assumes that the business has to be registered but not authorized.
For any self-employed work, it is necessary to fill out the Fragebogen zur steuerlichen Erfassung with your tax office. This is specified in §138 AO. I can't find information about a concrete fine, but misdemeanours are generally fined with between €5 to €1000, in proportion with the severity.
As a self-employed person, you are required to file taxes. Delayed tax filings are penalized (see §152 AO) with 0.25% interest per month on the due tax (at least €10 or €25 per month), but is capped at €25000. However, the surcharge can be dropped if no tax is owed. Note that without any tax filings, the tax office is required to estimate your earnings – and is allowed to assume the “worst case” of maximal reasonable earnings (§162 AO).
You are required to inform your health insurance about any changes to your employment, including taking up self-employment. If you are insured through statutory health insurance, they will recalculate your past insurance premium. The good news that premiums depend on your income, so low additional income will lead to moderate additional payments.
If you draw any kind of public benefits or social security payments (including Bafög or Arbeitslosengeld I/II), you must notify the respective office. You may be required to repay part of these benefits (with penalties). However, this will depend a lot on how much you earned.
Given that we're talking about low sums, there might be some exceptions from having to register as self-employed.
If your activity were revenue-neutral or -negative, there might be an argument that it's not a business but Liebhaberei, i.e. a hobby (but it depends on the details). Services as part-time tutor, artist, or caregiver might be tax-free for up to €3000/year (but it depends on the details).
That the self-employed work was carried out through a computer makes absolutely no difference.