what entomber stated is actually relevant regardless of whether you consider that an option or not although i do agree this is something that you could have thought up on your own.
getting "chuffed" at a response and feeling the need to generally complain about it does not help anyone.
on a budget of basically zero you do not have a whole lot of options available to you, but i've outlined the ones you do have.
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the simple truth of the matter is that it is not uncommon for laptops to have very poor speakers, with a reasonably low maximum volume being a common issue. sometimes this is a hardware issue where the speakers and amplifiers used are not meant for high output and sometimes this is a software issue where different/better drivers can help out.
by identical do you mean an EXACT match or just a model in the same lineup as the one you own? it also is not uncommon for the different models in a series of laptops which are almost identical to have minor changes such as using a slightly different audio chipset and using different drivers.
as far as using drivers from a different laptop model with your own laptop or basically drivers not officially supported for your model... if it is for the exact same audio chipset... they could certainly work and in fact some people do use such drivers to enable (unlock) some things such as dolby headphone on laptop models which do not officially support it but have a chipset which does. it could work, or it may not and have bugs, issues or cause driver clashes/freezing in some extreme cases or perhaps cause issues with your hardware if it is capable of pushing it harder than designed. in some cases this can be a solution but it is not guaranteed to work and of course is outside of any type of warranty if an issue does arise.
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so what are your options besides different drivers?
well assuming that you already have already tried running your audio program volume at 100%, are running your windows volume at 100%, all settings on volume mixer are set to 100% and still have low output of sound...and also assuming you do not have any sort of hardware failure like a failing amp or speakers.....
you could try using VLC media player to play your files which has an option which boosts volume. although that can cause issues with blown speakers see
http/en.community.dell.com/support-forums/laptop/f/3517/t/19492918 for details on this.
likewise you could try one of the various volume booster applications which would be similar to the above but would work with all applications. like the prior it can also potentially blow your speakers.
generally, anything which is capable of pushing your speakers to their limits can also potentially destroy them. it is always best to use the officially provided drivers and limits since they were set for a reason. going above and beyond is not covered by warranty at all and depending on what hardware is used and what files you play, for how long at what levels could potentially cause speaker damage.
as stated by entomber, the best way of getting around the internal speaker volume limits is to use an external speaker or headphones.
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now, some audio files or streaming movies or dvds are recorded with a rather low sound output. boosting these specific titles (and turning on/off boosting MANUALLY for select files which do not play loud) might be safe.
for instance i know that certain movies need 10-20% more volume level to play right than other titles which are recorded louder.
in this particular case you may be okay using a volume booster of some sort, otherwise i would be cautious about using a booster unless you are not worried about your internal speakers.