The short answer to your first question is 'Yes !'. These capacitors are all on their way out and when they finally let go your mobo will stop working.
However, if your soldering skills are any good capacitors of this type - electrolytic capacitors - are not too difficult to replace as they are not surface mount. You would need to remove the mobo, source replacements - which should not be too difficult, remove the old ones by de-soldering carefully and solder new ones in place.
Sourcing replacements is made easier by the fact that electrolytic capacitors normally have the value printed on the case. There are two parts to this - the capacitance and the voltage. The capacitance is normally expressed as a number of uF (microfarads) and the voltage as V (volts). While the values are not normally too critical do not use a lower voltage rating than the one of the old one, but a slightly higher voltage rating would be OK. For example, if the old one was rated at 12V you could replace it with one rated at 16V but not with one rated at 5V. The other important aspect of electrolytic capacitors is that they are polarity sensitive. One terminal is always clearly marked either +ve or -ve and they must always be connected with the correct polarity. If it is to be used on a +12V rail, for example, the +ve terminal must always go to the +12V side and -ve terminal always go to the ground (0V) side. If you get this wrong their service life can be measured in milliseconds once you re-connect the power !
While it is your decision, as I said replacing these is not too difficult, it may be time to bite the bullet and replace the computer.